A whole slew of good answers there ... please find below where we are to date - with highlights on those outstanding.
1. Taunton (past), Didcot (present), Teignmouth (future?)
- Rail bypasses
2. Taunton, Preston and Froghall
- Canal ends
3. Taunton, Wareham and Manuel
- Heritage lines joining main lines, but no practical regular services which could be useful to
Minehead (pop. 12,000), Swanage (pop 10,000), Bo'ness (pop 15,000)
4. Taunton, Ilfracombe and Meeth
At one time, terminuses of trains from Barnstaple (sneaked in while I was summarising

)
5. Taunton, Davenport and Hinkley
Closed locomotive works
6. Taunton, Basingstoke and WokingStated as flying junctions but I think I have something else
7. Taunton, St Austell, Barton-on-Humber8. Taunton, Exmouth Junction, Melton Constable
Railway Concrete Works
9. Taunton, Lisieux, Konigslutter
Towns twinned