From the very beginning trees have a very important role in our Hindu scriptures.
Dev Daanav Gandharvah Kinnar Naag Guhyakah,
Pashu Pakshee Manushyaashch Sanshrayanti Drumaan
Means - God, demons, Gandharv, Kinnar, Naag, Yaksh, Pashu, Pakshee, Manushya always take shelter under the trees.

Some trees have been described on and off.

Ashwatth or Banyan or Peepal Tree
Ashwatth is known as Vat or Baragad tree (Ficus benghalensis). At other places it is called Peepal tree too.

(1) When Maarkandeya Jee saw the Deluge he saw Naaraayan lying on a leaf of a banyan tree in an infant form in the Pralaya waters.

(2) Shiv as Dakshinaamoorti is nearly always depicted sitting in silence under the banyan tree with Rishi at his feet.

(3) Garud Jee, when felt hungry, his mother Vinataa directed him to his father for his food. Kashyap Jee told him to go on an island and eat elephant and tortoise. So he went there lifted them in his paws and looked for some place to sit and eat them comfortably. He found a banyan tree whose branched were spreading 100 Yojan long, to sit upon; but as he sat upon it, its branch was about to break, so he quickly ate both of them and threw the branch in a locality of a tribe.

(4) There is a Neel Parvat in the North of Sumeru Parvat. It has golden peaks among which I liked the four peaks the most. One of them has a Banyan tree, another has a Peepal tree, another has a Paakar tree and another has a mango tree.

(5) Also in Hindu culture, the banyan tree is also called Kalp Vriksh meaning 'wish fulfilling divine tree'. It is worshipped on many occasions. There is a Vat Saavitree Vrat on Jyeshth Amaavasyaa and married women worship Vat Tree for the long life of their husbands.

(6) The ancient Hindu scriptures speak of the Universe as an inverted Ashwatth or banyan tree with its roots in the Higher Worlds of Sat-Chit-Aanand (Existence-Consciousness-Bliss) and its branches in the many lower worlds that have been created. The world tree motif is present in many other religions and mythologies too.

(7) Read a story about the Ashwatth tree and Shani Dev.

(8) Kath Upanishad, II, iii, 1 - "Yam says about the world - “This is an eternal Ashwatth Tree whose root is above, but its branches are downward. It is He that is called the Bright One and Brahm, and Immortality, and in Him are all the worlds established, none goes beyond Him. This is That you seek for."

(9) Neelaarudra Upanishad, 3 - "This that comes is He that destroys evil, Rudra the Terrible, born of the tree that dwells in the waters; let the globe of the storm winds come too, that destroys for thee all things of evil omen.

(10) Bhagvad Geetaa, 15.1 - Here the Ashwatth tree is referred to banyan tree, not to the Peepal tree - "The Blessed Lord said - "There is a banyan tree which has its roots upward and its branches down and whose leaves are the Vedic hymns. One who knows this tree is the knower of the Ved."

Ashwatth (Banyan) - A Sacred Tree
Ashwatth tree is considered very sacred tree in Hindu religion. People worship this tree on special occasions as well as even daily.

(1) Ashwatth, literally literally means "where the horses stood" (Ashwa means horse and "tha" means "one that stands"). In ancient times horses were the main means of transportation, and perhaps every town or village boasted a Peepal tree to give comfort and rest to travelers.

(2) In the Bhagvad Geetaa, 15:1, Krishn says: "Of all trees I am the Peepal tree, and of the sages  I am Naarad. Of the Gandharv I am Chitrarath, and among perfected beings I am the sage Kapil. (10:26). In Geetaa, it 15th chapter opens with the name of this tree saying about it that Peepal tree's roots are very deep and they must be cut by detachment.

(3) Shankaraachaarya Jee also interprets this tree as a cosmos. A means "no" and "Shwa" in Sanskrit means tomorrow, and "tha" means that stands; so A+Shwa+tth means which is not the same tomorrow. The same is true for the Universe.

(4) There are also other hidden symbolic meanings of this tree – one such meanings is narrated by Bhagwat Shah of Pushtimaarg. The Peepal tree represents the tree of life and is sacred in Hindu Religion. It supports life of all sorts and is famous for its long life. The Peepal tree also has the property to purify air.

(5) Normally all temples house a Peepal and a banana tree in their compound.

(6) Worshipping Peepal tree gives relief from Shani's (Saturn) affliction;

The Great Banyan Tree of India
The great Banyan tree (Ficus benghalensis) is located in Aachaarya Jagadish Chandra Bose Indian Botanical Garden, Howrah, near Kolkata, India. It was the widest tree in the world in terms of the area of the canopy and is estimated to be about 200 to 250 years old. It is mentioned in Indian history that once an army stayed under its shade. This Great Banyan tree is the largest known in India, perhaps in Asia. There is no clear history of the tree, but it is mentioned in some travel books of the 19th century. It became diseased after it was struck by lightning, so in 1925 the middle of the tree was excised to keep the remainder healthy; this has left it as a colonial colony, rather than a single tree. The Great Banyan tree is over 250 years old and in spread it is the largest known in India, perhaps in Asia. There is no clear history of the tree, but it is mentioned in some travel books of the 19th century. It was damaged by two great cyclones also in 1884 and 1886, when some of its main branches were broken and exposed to the attack of a hard fungus. With its large number of aerial roots, The Great Banyan looks more like a forest than an individual tree. The tree now lives without its main trunk, which decayed and was removed in 1925.

A 330 meter long road was built around its circumference, but the tree continues to spread beyond it. The circumference of the original trunk was 1.7 meters and from the ground was 15.7 meters. The area occupied by the tree is about 14,500 square meters (about 1.5 hectares or 4 acres). The present crown of the tree has a circumference of about 1 kilometer and the highest branch rises to about 25 meters; it has at present 2880 aerial roots reaching down to the ground.

Kalp Vriksh and Paarijaat Vriksh from Saagar Manthan
When Saagar Manthan waa done to extract Amrit and Lakshmee, two Divine trees, a Kalp Taru (Kalp Vriksh) and a Paarijaat Vriksh also came out from that Saagar Manthan. Both Kalp Taru and Paarijaat trees were planted in Indra's Nandan Van (garden). Kalp Taru fulfills all desires, and flowers of Paarijaat Tree never fade away. Later Krishn brought the Paarijaat tree to Dwaarakaa for His beloved wife Satyabhaamaa, and the same went back to Nandan Van when Krishn left Prithvi for His own Lok.

Tulasee Plant for Vishnu
(1) Tulasee plant is a well-known sacred plant normally found in all Hindu households. All women, even men too, worship it daily with water, Dhoop, Deep, Rolee and Akshat. Importance of its worship is multiplied in Kaarttik Maas of the Hindu Lunar calendar.

(2) Vishnu Bhagavaan does not accept anything (any food item) without Tulasee leaf. That is why no Hindu house is found without Tulasee Biravaa (plant). It is still strange that although every house has Tulasee plant, Tulasee plant is not found inside the house. Tulasee plant is always planted outside the house or in the courtyard of the house.

(3) Tulasee leaves garland is offered to Badaree Naath Jee and people get it in Prasaad.

In fact the whole Tulasee plant is very important and worth worshipping for a Hindu. Its leaves and flowers (Manjaree) are for Vishnu, its leaves and roots are for medicinal uses, its wood is used for making beads to make a rosary for Jap.

Bel and Dhatooraa Tree for Shiv
Bel tree is another tree which is used in Hindu worship. Bel fruit and its leaves are offered to Shiv whenever he is worshipped. Even deities worship this tree. All the holy places of pilgrimage are located at the roots of Bel tree. A pious person who worships Shiv in his Ling Swaroop installed at the roots of Bel tree attains Salvation. By performing the Abhishek on Shiv at the roots of Bel tree, one can attain the Punya of having holy dip at all the places of pilgrimage. Mahaadev is pleased to see a Bel tree which is watered properly and nurtured. A seeker can attain Shiv Lok by worshiping Bel tree with Sandal, flowers etc and his progeny flourishes. One can attain enlightenment by lighting lamps at the roots of Bel tree. All the sins are destroyed by worshiping this tree. Punya and wealth can be attained offering food to the devotees of Shiv. Aadi Shankaraachaarya has explained the benefits of offering Bel leaves to Shiv in his Bilvaashtak,

Dhatooraa fruit is also offered to Shiv while worshipping him.

Shamee and Mandar Trees
Both these trees, Shamee and Mandar Trees, are blessed by Ganapati that his father Shiv and his own worship will not be complete without these two trees. When any sacrifice (Havan or Hom) is organized in Shiv or Ganapti temple, priests rub only the Shamee tree wood to start fire. And no worship of Shiv and Ganapati is complete without Shamee leaves and Mandar flowers.

It was the Shamee tree on which Paandav kept their weapons before they entered Viraat Nagar to spend their A-Gyaatvaas (incognito) period of exile.

Shamee tree is worshipped on Dashaharaa day (Aashwin Shukla 10) also.

Banana Tree
Banana tree is also very common tree in temples and in houses for worshipping. People worship it on Thursdays. People decorate their Poojaa places with the cut banana trees.

Krishn and Two Trees (Yamalaarjun)
This story comes in Bhaagvat, 10/p4. There were two sons of Lord Kuber - Nalakoobar and Manigreev. Once they were sitting on the banks of Mandaakinee River and drinking wine. Later they started playing with women inthe river too. In the meantime Naarad Jee came there. The Apsaraa were their clothes but these Yaksh did not, Naarad Jee cursed them to be trees. When they asked his for his forgiveness, he said that they will be freed from his curse in Dwaapar Yug (after 100 Divine years) when Krishn will be incarnated and He would free them. They were born as trees and became famous as Yamalaarjun. Krishn freed them from this Yoni.

Aamalaa and Ashok Trees
Both trees are mentioned heavily in mythology in various references. Padm Puraan gives the importance of Aamalaa tree and fruits at two places - Padm Puraan, 1/31; and Padm Puraan, 5/13. Ashok tree has been mentioned in Raamaayan and Maanas. Seetaa lived in Raavan's Ashok Van under an Ashok tree. Even Buddha, who is considered an incarnation of Vishnu, after Krishn, was born under this tree in Lumbinee. Mahaaveer Jee, who was the last Teerthankar of Jains, also renounced the world under this Ashok tree in Vaishaalee.

Special Trees
--There is one Aamalaa Tree (Indian Gooseberry) on the sea shore where Aadi Shankar showed his power to rain golden Aamalaa fruits for an old woman. That tree is known as "Tamaalam" is found only along the seashore. It is a rare tree. This is the most widely spread tree and it has countless branches. (See its description) Read why Aamalaa is a holy tree here at Vishnu and Tulasee.
--Some trees have three leaves attached to their stalks, they are - Palaash, Dhaak, and Bilva Patra.
--Everybody knows that Neem tree leaves are bitter. There is one Neem tree on the banks of Narmadaa River, near Nareshwar temple, some 70 Kms away from Baroda, in Gujaraat. Here lived a saint Rang Avadhoot. He used to sit under that tree. Because of that saint's company that Neem tree's leaves are sweet within its 20 feet radius, while rest of its leaves are still normal (bitter).

A Thought
Then why do we animals have definite life span, longevities and die as we age? Why can we not clone ourselves into immortality like plants and trees? Even our cells cannot go on dividing and reproducing themselves beyond about 40 cycles. The answer to this puzzle came from an understanding of the mechanism of genetic duplication in our chromosomes.

Each time a chromosome divides and makes a copy of itself, a small bit of its end (called the tail end or telomere) is lost. Thus, after a set number of duplications, the progressive telomere shortening leads to the dead end. Understanding telomere biology and how cells are ‘immortalized' in cancer (through the enzyme called telomerase) came from the work of a large number of people, culminating in the work of Drs. Elizabeth Blackburn and Carol Greider (who won the Nobel in 2009 for this work). That plants have a somewhat different mechanism of ageing became apparent soon enough, and Dr Barbara McLintock (who won the Nobel for discovering how genes can 'jump' or transpose themselves) called it ‘chromosome healing'.

We now understand a little better that ageing and telomere action in plants are different from animals. When we talk of an animal's life span, we talk of the survival of its entire body, but in a plant, there is comparatively only a rudimentary body plan. Plants grow in a modular form - individual modules being roots, shoots and branches, leaves, inflorescence and such.

As leaves age and die off, the rest of the plant does not. Also, plants grow using what are called vegetative meristems — these are undifferentiated stem cells that can regenerate into the entire organism. Thus, one can pick up a twig or a branch and grow the entire tree, or graft into another and make a new tree with added features. And cell death is not the death of the entire organism. A lucid, readable review of the subject is published by Drs J Matthew Watson and Karel Riha of Vienna, Austria. Titled “Telomeres, Aging and Plants: From Weeds to Methuselah: A Mini-review”, it is published on line on April 17, 2010 in the journal "Gerontology". Those interested may go to google.com, type out the above details and download the entire article free.