These are some games I know of that do this:
Wizardry 1-2-3 on most non-console platforms; in fact, Wizardry 2 and 3 on most computer platforms are entirely unplayable without Wizardry 1 data as you can't create new characters in them
The Bard's Tale (classic) 1-2-3. Dragon Wars, while not related, can also import and convert data from the three Bard's Tale games. The first Bard's Tale can also import and convert data from Wizardry 1 or Ultima 3 on some platforms despite them being unrelated.
Might and Magic 1-2
White Knight Chronicles 1-2 is a special case; the sequel came with a remastered version of the first game, and will load data from the first game, but if you never played the first game, you have to play through the remastered version before playing the sequel.
The AD&D Gold Box games were already mentioned, as was Golden Sun 1/2