There are many Vrat in which Vrat is completed after worshipping the Deity and listening of his or her story. Here are some of those stories which are heard and told on Vrat days.

Ravi Vaar (Sunday) Vrat Kathaa
Som Vaar (Monday) Vrat Kathaa
16 Som Vaar (Monday) Vrat Kathaa
Mangal Vaar (Tuesday) Vrat Kathaa
Budh Vaar (Wednesday) Vrat kathaa
Brihaspati Vaar (Thursday) Vrat Kathaa
Shukra Vaar (Friday) Vrat Kathaa
Shani Vaar (Saturday) Vrat Kathaa

Budh Ashtamee Vrat Kathaa - Vrat on Shukla 8th falling on Wednesday
Mangalaa Gauree Vrat Kathaa - Vrat kept on all Tuesdays in Shraavan Maas
Pradosh Vrat Kathaa - Vrat kept on Pradosh days
Som Pradosh Vrat Kathaa - Vrat kept on Monday Pradosh

Karavaa Chauth Vrat Kathaa - Vrat kept on Kaarttik Krishn 4th
Ahoee Ashtamee Vrat Kathaa - Vrat kept on Kaarttik Krishn 8th
Nava Raatri Vrat Kathaa - Nava Raatri
Shiv Raatri Vrat Kathaa - Vrat kept on Maagh Shukla 14th

The following Ekaadashee are given in detail with their Vrat Kathaa --

Ekaadashee - Aparaa (or Achalaa) - Jyeshth Shukla
Ekaadashee - Dev Uthaan (or Prabodhinee, or Haribodhinee)  - Kaarttik Shukla
Ekaadashee - Indiraa - Aashwin Krishn
Ekaadashee - Kaamadaa - Chaitra Shukla
Ekaadashee - Kamalaa - Adhhik Maas Krishn Paksh
Ekaadashee - Mohinee - Vaishaakh Shukla
Ekaadashee - Mokshdaa - Maargsheersh Shukla
Ekaadashee - Nirjalaa (or Bheem, or Paandav) - Jyeshth Shukla
Ekaadashee - Parivartanee (or Padmaa, or Jal-Jhulaanee, or Jayantee, or Vaaman) - Bhaadrapad Shukla
Ekaadashee - Saphalaa - Paush Krishn
Ekaadashee - Shat-Tilaa - Maagh Krishn
Ekaadashee - Shayanee (or Shayan, or Dev Shayanee) - Aashaadh Shukla
Ekaadashee - Vaikunth (or Vaikunthinee, or Varoothinee) - Vaishaakh Krishn Paksh