I have played a lot of 360 games. 

So far I think that some of the best achievements are in Call of Duty 4.   You can get them all without having to go online.  There is a nice number that you can achieve just by going through the game normally and then there is the set when you turn the difficulty up to Vetran.  Finally, it has achievements that you can play the game through multiple times to get.  The only thing I wish they had is some achievements that you could get either online and offline simultaneously...

I think Halo 3 has the best achievments list. There are a good number of online ones but for people with no gold subscription they are only missing out on about 50 points. I have never completed a halo game on legendary before but the achievments made me go all out for the full 1000/1000 which i admit is pretty sad but i enjoyed it:)

The orange box has good achievments too, although launching the garden gnome into space in episode 2 is just too far for me. It's cool if you can do it though!

I think that Crackdown has got it done well. You can literally just play the game, and having fun, and not realise that you're actually doing the achievements.

Mass Effect.

Unlike every other game, the achievements actually DO something for you in game. There's nothing like unlocking the Power Gamer achievement, and getting more EXP per action, or Kill Enemy with X Gun 150 times, or Use Biotic/Tech Y times, allowing you to have those skills, regardless, on your next playthrough.

*really likes the mass effect ones as well*

crackdown had some really crazy ones
halo 3 was good except for online acheivments

Crackdown was my second choice.  I spent weeks combing the city looking for my last visible orb.  And then one day, standing on the top of a building in Shei-gen I saw it gleaming at the second level of the tallest building on the west side.  There was a very high degree of satisfaction when I got it...  500 orbs is a lot!

Dead Rising.

No particular achievement is worth more than another, but going after them really makes you explore the game, and take chances.

 And some of them are really tricky. Have you ever tried the 7 days alive? Man, that demanded almost 30 hours of real time gameplay. My 360 would blow!

Concerning the Call of Duty 4 achievements. 3 words

Mile High Club

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Almost 150 loadings, 4 times I almost reached the bloody double door. 2 times I shot. The forst one at the leg. I wanted to cry but i simply loughed. These guys have a sick sense of humor!

The second time (after 30 loads- I was warm enough) I shot the bastard in the head!