The eastbound Capitals United from Swansea [some capital
] to Paddington is fast from Swindon. This makes it possibly the only train to skip Reading. 70 miles away, the 0520 from Bristol, the (former?) 0608 from Westbury, skips Bath, which was until May effectively a compulsory stop for all non-diverted traffic.
Back home, on the c2c route, most trains call at Basildon, apart from a few peak services (including the 1700 and 1730 from London), and literally a couple run fast through Tilbury Town and East Tilbury. In years gone by though, a partially skip-stop pattern existed in Southend; to give an example, in the June 1996 timetable the 1726 from London did not call at Chalkwell or Southend Central.
Another one would be the Harwich route, on which trains timed to meet ferries often do not serve the local stations on the route. And speaking of ferry connections, trains connecting with Fishguard ferries skip all manner of stations, with the 1057 from Cardiff calling only at Llanelli and Whitland and thus skipping Bridgend and Port Talbot Parkway and using avoiding lines to skip Neath, Swansea and Carmarthen.