While not a universal glitch, our FF3 Cartridge (SNES) had a glitch where if Relm painted a Zone Eater... The game would screw up. 99 of all the best items in the game (Atma weapons, cursed shields, red shurikens, etc)
Keeping Alucard Equipment in the beginning of Castlevania: Symphony of the Night.
Succubus Soul glitch in Castlevania: Dawn of Sorrow.
More to come if I remember.
Edit: Keeping Alucard EQ is a sit sounds, you get to keep it via skipping the cutscene by force where you lose it all. Normally, you'd walk in, Death talks to you, then steals your EQ. If you play on super Luck mode (all stats 0 except Luck is 99, and HP is 25), you need to gain one level and make sure you have enough DEF to take a hit, and live. Have a Warg bite you in the room before hand, sending Alucard flying very very VERY fast across the screens, shooting past the cutscene.
Succubus Glitch is... weird. Basically, you have the Succubus Soul (Bullet type, so ^ + Attack = special move) and you have a dagger that can pull off the backstab special attack. You activate the SS, which is a small animation of Soma lunging forward maybe have a character sprite, and biting whatever's in front of him. He gets a special red aura around him, making him invincible for a set period of time. When he's in mid lunge, you use the dagger's SA, which prolong's the effect. OK, so you stab 2 or three times to prolong the effect (it wears off quickly), then do the SA again, and viola, when the red aura disappears, all actions you are doing stop. So, you did the teleporting backstab, right? Bam, you can travel through normally impassable walls and stuff. Now for teh glitch to REALLY get weird. When you do the backstab attack, you can lodge yourself in a wall, sending Soma flying forever and ever upwards for a long time. When/if he stops, you move left or right or something, and then you appear in a random room (hopefully. Otherwise, you just wasted 15-20 minutes), and you have suddenly collected skills and abilities and weapons and items you should never ave at this point (Or ever! You can get skills that belong to the other character modes this way, including Alucard's bat transformation that doesn't go away with a NG+!)