In trying to think of game series with consistent worlds/stories that went beyond a trilogy that I've played... I came up with a few.
Honorable mention to Final Fantasy, although it doesn't do one consistent world. For the record, I stuck with it for 1 through 9.
Firstly: Dragon WarriorQuest, of which I played the first 4 games. After that I couldn't find any localisations and gave up (next thing I know I'm seeing Dragon Quest 8 in game shops, when I never saw 5, 6 and 7 come out).
Second: Phantasy Star. I sort of retroactively played the first two on GBA, but back in the 16-bit era this series was the primary reason I saved lawn-mowing money to buy a Genesis. I was dedicated to Phantasy Star 3 despite its shortcomings... the branching possibilities across generations of protagonists was an amazing concept at the time... Phantasy Star 4... still holds up to this day. It's the Chrono Trigger of the other side. Terrific game.
Too bad about that Online crap. Sad to see a great series die like that... but at least it wasn't as undignified as what Final Fantasy has become.
Next: Star Wars: Dark Forces. Cheesy as the story of Star Wars Chuck Norris is... I love all 4 of these games and I want more. I especially love the titling system and would love to see it get even more convoluted. (Dark Forces, Dark Forces 2: Jedi Knight, Dark Forces 3: Jedi Knight 2: Jedi Outcast, Dark Forces 4: Jedi Knight 3: Jedi Academy... can I get a Dark Forces 5: Jedi Knight 4: Jedi Academy 2: Desann Strikes Back?)
Finally: Fallout. So far I count 5 titles (1, 2, that Chicago spinoff, that DC spinoff, and the third main title set in Vegas... there are no others to date. No. Shut up. Never happened)... I'm impatient for more and hope it never ends.
So it depends heavily on the franchise, and consistency therein. Most of 'em are one-and-done, sometimes there's a worthy sequel to be had, occasionally a trilogy is called for... but once in a great while a franchise comes along that I'd love to see go on forever.