These are probably all outlined on TV tropes already, but here goes.
Almost any NES and SNES era RPG, and thus pretty much every later RPG game where you can traverse a world map. Going to the end of the map (usually needs to be done via boat or airship) will often cause you to respawn on the other side, no matter where you do this. This means that the planet on which the game takes place is shaped like a donut.
Another one common to RPGs especially, but can appear in platforming games as well are objects such as low fences or tress that you should be able to go around or over, but can't. They're often conveniently put in places to keep you from going to the edge of the map
Also, any sequel to a game that stars the same character(s) as the original. Most of the time, all of the items and skills that a character obtained in a previous game vanish to give a fresh start in the sequel. This is also especialy apparent in RPGs (Final Fantasy X-2 and Paper Mario: The Thousand Year Door being examples), but appears just as often in other games. An explanation may be given, such as the character being shipricked and losing all their equipment (a la Zelda: Link's Awakening), but just as often everything is gone mysteriously and must be regained.
Next come cutscenes. Outside of the actual gameplay, characters are able to perform amazing feats of strength and agility, or unable to do such things that they could while not in a cutscene. Even worse, a character might just watch in awe as something terrible happens, that could have been prevented if they took action. Cloud is suddenly frozen in place while Sephiroth descends from the ceiling and kills Aeris. This works in reverse too (sorry Final Fantasy, you're just too easy to quote), such as the summons in FFIX being immensely more powerful when you're not on the battle screen.