Fed's starter-ship (Miranda-class). If you dismiss this ship, you can never get it back. This may also be true for the KDF starter (B'rel), but I'm not certain. There has been Dev talk that they "some day might" add a way to reclaim the Miranda, but it's all wishful thinking at this point.
Basic Flagships (Odyssey and Bortas) that were given away for the 2-year event. You can always purchase the C-Store variants, but the freebees are truly gone for good once dismissed.
Legacy Ships: Delta Flyer, T3 Excelsior, T3 Nebula. These ships used to be available directly in-game (The latter (DF) originally via a quest, the former two (T3 E/N) from the ship vendor via EC), and if you had them when they were pulled you still have them. If you dismiss one of these legacy ships now, you can only get them back again via the C-Store.
LockBox Ships: Jem'Hadar Bugship, Cardassian Galor, Ferengi D'Kora. If you dismiss one of these they are also gone for good. The first two are currently retired. The only place to (maybe) still find one is on the Exchange. The Bugships are rare/expensive (~500M EC), the Galor are fairly common (~80M EC). The D'Kora is also available on the Exchange (last I bothered to look, for ~150M EC. I expect that to go down, if it hasn't already.). Of course, since not (yet) retired, this last one might also still be re-acquired from another Lucky LottoBox draw.