Godan Express: गोदान एक्सप्रेस - प्रेमचन्द की लेखनी ने रची यह अनुपम कृति, ये जोड़े मुंबई से पूंर्वांचली संस्कृति ।। - Saurabh

This is going to be a long post - I'll try to spread it over 2-3 posts.
State-wise list of abandoned/non-functional lines (Going South to North - Some states really do not have any notable abandoned lines, in those cases, I've highlighted some small bypass lines that were abandoned).
Kerala -
Meter gauge - Cochin State Forest Tramway - Thrissur-Parambikulam (dismantled)
Narrow...
more...

gauge and Mono-rail - Kundale valley railway (near Munnar, Kerala) - Washed away in floods.
Tamilnadu -
2'6" narrow gauge - Morappur-Dharmapuri - Dismantled. Line originally extended to Hosur. Dharmapuri-Hosur is now a BG line.
2'6" Narrow gauge - Tirupattur-Krishnagiri - Dismantled
2'0" Narrow gauge - Kulasekharapatnam light railway - Tiruchendur to Kulasekharapatnam/Tissianvilai - Dismantled
Meter gauge - Rameswaram-Dhanushkodi (dismantled) Pamban- Dhanushkodi (washed away in a cyclone in 1964)
Karnataka -
2'0" Narrow gauge - Tarikere-Narasimharajapura tramway - Dismantled.
2'0" Narrow gauge - Tadasa-Hebbe tramway - Dismantled
Ex-Andhra Pradesh (including Telangana) - No real major abandoned railway in both states, so combining them
Broad gauge - Tsunduru-Vejandla chord line (dismantled)
Meter gauge - Macherla - Nagarjuna sagar dam construction line (dismantled)
unknown gauge - Godavari river tramway - Operated on the East bank of the Godavari river, near Bhadrachalam. Dismantled in the 1800's.
Maharashtra -
Meter gauge - Chinchwad-Mulshi and Mulshi-Kolad/Roha construction railway used by Tata Power for constructing and maintaining the Mulshi dam. Dismantled now.
2'6" narrow gauge - Darwha-Pusad - Branch line on the Murtizapur-Yavatmal Shakuntala railway (dismantled)