It would be helpful to know what system and what are some games you like but here are a few thoughts (lots of repeats from pervious posts though). I'm a PC guy so these are all for that system. Most of them are older, you just rarely see them being made anymore unfortunately so you'll need a certain level of tolerance for bad graphics. Also you will probably need Dosbox or to download them from GOG.com. GOG is a great sight for getting old game btw but the selection is still fairly limited. There are some RPG's there that I've never played that are turn based.
Ultima series (3-7 are the ones to target).
Wizardry series (only played 6, 7 and 8 but previous ones are highly regarded as well). Less story oriented and more hack and slash but they do have stories and conversation. Just a bit limited. Older ones I think are pure dungeon crawls.
Spiderweb game (Exile, Avernum, Generforge, etc). These seem to all be highly inspired by the Ultima series.
Might and Magic games (Heroes of Might and Magic is more of a strategy game though). Have been like 9 of these I think. Can't really remember which are the best ones anymore.
Fallout 1 and 2
Balder's Gate series (not really turn based but can come really close to it with auto-pausing. Can pause anytime also). Also Dragon Age is in a similar vain but feels a little less turn based. Might want to check that out.
Temple of Elemental Evil
Neverwinter 1, 2 (like Baldur's gate series with pausing)
Arcanum
Gold Box D&D games - there are a ton of these
Bard's Tale series (the original 3 not the new one). Similar in style to wizardry games.
Wizard's Crown series. Great game but very old, very combat focused but the combat is very involved.
Realms of Arcania - only played this a little so not sure of how good it is but seems good
If you don't care about graphics (they are all ascii but some now have some tilesets) you might also be interested in the rogue-like style games. There are of offshoots so it's best to just do a net search. Mainly dungeon crawls but they have a lot of depth and replayability. Some popular ones in ADOM, Crawl, Angband, Nethack.