Here's how some of the SaGa games handle time:
* SaGa 3: There's time travel. The world is flooding, so the water level is higher in the future and lower in the past. I believe the eras are 15 years apart, so the difference between past and future is only 30. Note that time doesn't pass in the alternate dimension, so time travel disappears in the entire later part of the game. (Chrono Trigger takes the time travel idea much further than SaGa 3 does.)
* Romancing SaGa 1: Time passes with each battle. Fight enough battles and the Event Rank (ER) increases; when this happen, things change, some quests close, and other quests open. ER is capped at 22, and the final quests requrie ER 20. (In the PS2 remake, the mechanic is a bit more complicated, with harder battles counting more.)
* Romancing SaGa 2: (Disclaimer: I haven't played this game.) There are certain "black screen" events. If you've cleared enough of them and/or fought enough battles, and you aren't on the final emperor/empress yet, a generation shift will occur; years pass, you get to choose a new emperor, and the emperor will inherit the abilities of the previous one. Furthermore, research will complete, and the arts learned in the previous generation can be easily taught to new characters.
* SaGa Frontier 2: The game consists of a bunch of events that appear on the world map. Choose an event, play through it, and you are returned to the map to choose another one, with new events opening up as you clear them. The events take place at different times in the world's history, ranging from 1220 to 1306. As characters get older, their stats change. (Note that it is possible to play events out of order; you might play an event where someone plot dies, and then follow up with an earlier event in which that character is still alive.)
Canuck_Cat: I'm a big fan of milestone time skips. By the time you reach certain story events, a certain amount of time has already passed in the game. Your experience along the way was just a condensed version of that time spent for your characters. For example in FF9, widely considered to have excellent pacing, [link with story spoilers]
the events occur over the course of 3 months, though the characters don't really take a break. You're welcome to slaughter 0-1000+ random encounter enemies between the town and the next dungeon, but only 1-2 days have past in that time.
Works find until you look at one particular part in Dragon Quest 5, where a character, in what feels like too short a time, gets married, gets pregnant, and then gives birth.
Incidentally, Dragon Quest 5 does have two major time skips during the game, where many years pass (think the first one is a full decade), and the first one has your character growing up during that time, albeit not in nice living conditions.
Phantasy Star 3 also has some time skips, where you marry someone, and then play as that character's son.
I hear Fire Emblem 4 also has a big time skip, and apparently modern FE games may do some of that as well.