Here's a list of things that annoy me in video games:
Game crashes - This is pretty much inevitable, and there's often no way for the programmers to prevent this from happening. But the number one thing that makes me rage in a video game is if the cartridge gets disconnected, there's a power outage (if playing a console game), the ROM crashes (if using an emulator), or the game just randomly decides to turn off, causing me to backtrack through hours of gameplay I just went through.
Chase sequences in platformers - When I'm playing a platformer, I like to take my time defeating enemies and figure out the puzzles, preferrring not to rush through everything quickly (which is probably why I'm not too fond of the Sonic games). When a platformer makes me chase after a certain character, it's basically forcing this speed element upon me. I'm playing a platformer, not a racing game. This seems to be especially prevalent in the 3D Mario games, like those segments in Sunshine where you have to chase Shadow Mario. Galaxy is filled with a LOT of them - not only the special comets where you race yourself, but the many levels where you have to race against penguins or a Boo, or catch Star Bunnies. Heck, even the fights against Bowser (and there are like 4 or 5 of these) involve chasing him just to hit him. Thankfully the game is pretty easy in general; otherwise these would annoy me to no end.
Overabundance of status-inflicting enemies in RPGs - So I'm going through a dungeon in an RPG. I come across some enemies. I fight them. Great, one of them paralyzed someone on my team, and now I have to use a healing item. The next battle, SAME THING HAPPENS. And then I run out of healing items and I'm screwed. Even if I have lots of healing items, this is still annoying, especially if the status problem hinders my character's performance in the battle and I can't easily run. I've run into this several times in the Pokemon games, because I swear, if I battle another stupid Bellsprout who uses friggin' Stun Spore for the umpteenth time... Which makes me thankful for the status problems that go away after a battle is over, as seems to be the case for most status problems in the early Final Fantasy games (except the super-annoying "Dark" status in FFVI, because I hardly ever have the item necessary to cure it because I forget where you can buy it, there aren't enough Relics which prevent that status for my entire party, Cure doesn't get rid of status problems, and the status itself makes physical attacks less likely to hit).
Can't skip cutscenes - Thankfully, most games let you skip a cutscene after you've watched it for the first time. Games that don't have this feature are super annoying because every time you die, you have to play through everything since the last save point, cut scenes included. Annoying especially since there are often long cut scenes right before boss fights, so if you save before a boss, encounter boss, sit through cutscene (which is fine the first time), battle boss, and die, you have to encounter the boss again and sit through the entire cutscene again before attempting the boss battle once more. If Kingdom Hearts didn't have this "skip cutscene" feature, I would hate the game, because that game has a RIDICULOUS amount of cutscenes, and long ones too (most of them are interesting to watch, though - the most boring ones happen to come right before boss battles).
Camera screw - This is a HUGE one for me. Basically, this is when a level, boss battle, etc. is way harder than it should be because the camera is never where you want it to be. Thankfully, games have (for the most part) gotten better with this with time, as more modern games typically have more intuitive camera controls, but this was frequently a nightmare back in the days when 3D video games were new - like in the N64 and PS1 era. I've heard of games that change camera angles mid-jump causing many a player to fall, automatically adjust the camera away from an area you're trying to focus on, not letting you control the camera when you really want to (I'm looking at you, Super Mario Galaxy), and in games with target locking, locking onto anything but the enemy I'm trying to target (Kingdom Hearts, WHY do you make me push the right and left buttons so many times just to target this Fat Bandit rather than the multiple weak Heartless around him that move around a lot?). But the biggest offender I've encountered in a game I've played thus far was Ocarina of Time, specifically during the fight with Twinrova's first form. You're supposed to reflect one witch's magic at the other one. Sounds simple enough. But you better be able to see both of them at once while one's attacking; otherwise you're screwed. It doesn't help that the two are flying around randomly overhead, while the camera likes to focus primarily on Link who is on the ground (even with Z targeting).
"Your character didn't jump, even though you clearly pressed the jump button" - This especially happens to me in 3D games that involve jumping (regardless of genre) - if I'm trying to take a running jump off one ledge to the next, if I want to jump off the very edge of the ledge, sometimes I'll press the jump button but the character will fall off the ledge rather than jump. That leads me to reattempt the jump from like an inch away from the edge of the ledge, which is not easy to do, and if I start the jump from too far back, there's no way I can make it to the next ledge. I've especially encountered this in the Kingdom Hearts games - it's like, "Come on Sora, what's so scary about jumping off the edge of a building? Banjo and Mario don't have any problem with it."
And by contrast you have Link, who will ONLY jump if he runs off the edge of a platform, and will always do so. I can't tell you how many times I've wanted Link to just drop off the edge of a platform, when he almost always either jumps off and lands in a spot several steps ahead of where I want him to land (especially annoying if I want him to land on a narrow platform directly below the one he's currently on, and jumping will make him overshoot the platform and fall into a bottomless pit), or hangs onto the edge of the ledge and gets back up before I can have him let go. Thankfully, games that have the Hover Boots avoid this problem, as Link won't jump off ledges if he's wearing these.
Ice levels - Few things are more frustrating to me in a platform or action adventure game than having my character slip and slide all over the place. In all the games I've played, I've never found it fun. Not to mention those same levels tend to have enemies that can freeze you solid, which in some games makes you lose a significant amount of health (Legend of Zelda 3D games, I'm looking at you). In fact, one of the ice levels I genuinely enjoyed was the one from Kirby's Dreamland 2, solely because of the hamster Rick who does not slip on ice. On the other hand, if you can skate on the ice (like in Super Mario Galaxy or Pokemon X/Y, especially the former because of the presence of a donut-shaped ice planet you can skate forever on, and also Ice Mario - this may be present in other 3D Mario games too), that adds a new level of awesome to an ice level.
Enemies that permanently steal/destroy your items Hooray, I am in possession of a super-rare item, or one there's only one of in the game! I can't possibly lose it, right? What, an enemy stole it from me? WHY YOU... It annoys me to no end when enemies steal or destroy items my character is holding, even though that process is quite realistic. For example, I was playing Pokemon Silver once and got to the part where Team Rocket takes over the Radio Tower, and I had to fight some burglars in the underground. One of the burglars had a Pokemon with Thief, which stole the Miracle Seed my Meganium was holding. In those days, a stolen item does not return to you after a battle, and there's only one Miracle Seed in the game. Bye-bye, one-of-a-kind item...
As a lesser example, in Ocarina of Time, there are fiery bats who charge at you, and if you're carrying a wooden Deku Shield, it will burn up and be destroyed. Thankfully, the first dungeon where these bats are found has a place to buy additional Deku Shields, but it's still annoying to go buy another one each time, especially since that's the only shield that will protect young Link from projectiles. And then Farore help you if you encounter one elsewhere later in the game, because then you have to go all the way back to a shop to buy a new shield. Oh, and in that same game, there are Like-Likes who will steal your items, but give them back when defeated. However, if there's a Like-Like near the edge of a platform over a bottomless bit, sometimes defeating it will cause the item(s) to fall into the pit so you can't recover them. Or, if you fall into said pit while the Like-Like still has your items, you can say goodbye to those items. Recently I lost a tunic because of this, and the only way out of it was to reset the game and lose two hours of dungeon-crawling.