Achievements
Likes:
-Adds Replay Value
-Nice pop-up sound
-Raises up your "High Score"
Dislikes:
-Makes people OCD 
-Achievement whores
-People will play games for the wrong reasons
-Achievement whores
-Online MP-only Achievements
 
Same could be said for Trophies except I don't see as many "Trophy Whores" as with Achievements.

it makes me OCD and do silly things i don't want to do just to get an S-Rank and it makes me buy games on the xbox 360 i might normally buy on the PC.

I hate it when they add achievements with insane goals just to add time-played to their game. For example, Forza 3 has a 80gs achivement called Soild Gold. You have to get a gold star on each event on the calander. So basically win every race in the game. Theres probably over 200 races. Laps vary from 2 to 15. Lap length can vary from 30 seconds to 5 minutes. Its just a giant time sink.
 
Also hate multi-player only achievements. Mainly because, many MP games fucking suck and I don't want to take the time to play your shitty online to get the achivements. Take Gears of War 2. Amazing game, can't wait for the 3rd. But sweet fuck thats the worst competitive multi-player ever. Throw in an achievement to reach the max online level and I'm going to resent it. I don't want to be forced to play MP features if I don't want too. I feel bad for people with Silver accounts who can't play and get the achivements.
 
I also hate it when they release DLC and add locked achievements to your card. Lets say I finish game, I have my 1000gs and I don't plan on touching it again. They come out with DLC with achievements, all of a sudden that game is no longer 'complete' on my card. I don't think its fair that because I don't want to buy the DLC that it should say my game is incomplete. They should have a way to separate it, maybe only add on those extra achievements once you download the DLC.

The only thing I dont like about achievements is when someone thinks they're better than anyone else because of their gamerscore. Yeah its cool that you got the mile high achievement. Doesn't mean you're the best player in the world.

I like the sense of progression it gives you.

when they're spelled correctly/ incorrectly.

I hate mandatory online multiplayer achievements. I try to deal with the idiots on XBox Live as little as possible but there are some achievements that are fun to try for that require jumping in the cesspool. 

I hate when "You beat the game!" achievements pop up before the credits role. They usually happen right when the ending cinematic starts, right after a huge climactic part, and it takes away from the experience IMO.

"I hate when "You beat the game!" achievements pop up before the credits role. They usually happen right when the ending cinematic starts, right after a huge climactic part, and it takes away from the experience IMO. "

I love achievements because they really make me strive to get the most out of the games I buy. After mining a game for all its achievements, I really feel like I've gotten my money's worth.

I dislike achievements which have clearly had no thought put into... like all achievements are story related... at least make an effort developers

I really don't like: 
- high-end multiplayer achievements (i.e. kill 10,000 players online) 
- difficulty setting achievements; it's lazy, and inaccessible to those who may prefer to play games on easier settings

@project343 said:

"I really don't like: - high-end multiplayer achievements (i.e. kill 10,000 players online) - difficulty setting achievements; it's lazy, and inaccessible to those who may prefer to play games on easier settings "

while I'm not hugely fond of having there be  a ton achievements tied to different difficulties...if all achievements were open to the  easiest settings it would completely go against the idea that it is an achievement.