Update: I've added Ninja Theory's Devil May Cry to the list of Xbox 360 games for which I've gotten all 1000 achievement points! 

Original Story: I want to clarify this right away: I’m not an achievement junkie. I don’t get an adrenaline rush from the distinctive bloop that accompanies the “achievement unlocked” message, and I don’t care about my gamerscore. Given those facts, it may seem strange that I have gone to absurd lengths to get every achievement in a small handful of games. These elite titles are the members of my 1000 Club. 

Achievements aren’t meaningless for gamers like me. I have been known to obsessively collect knick-knacks, grind levels, and accrue percentage points toward total completion. I may not care about the gamerscore side of the equation, but I’m always looking for fresh goals and objectives that will give me an excuse to spend more time with awesome games. Getting all 1000/1000 points is mainly of symbolic importance; by getting every achievement, you have likely seen almost everything that the game has to offer…or at least the parts of the experience that the developer thought were important.

Doing this with every title I play would just make gaming feel like a chore. The members of my 1000 Club are the standouts that, for various reasons, inspired such obsessive loyalty from me that I was compelled to explore their every nook and cranny. Those things will be different for each gamer, so what makes you decide to induct a game in your 1000 Club?

Devil May Cry (Update: 3/25/13)

To get the full 1000 in DMC, you need to be okay with playing through the whole game six times. There are achievements for playing on Nephilim, Son of Sparda, Dante Must Die, Heaven or Hell, and Hell and Hell difficulty. You have to play each of them because they unlock sequentially; there's no "beat one and the earn the achievements for the lower levels." Plus, there's an achievement for getting all SSS rankings on Nephilim, which means you'll probably have to play through all of those missions again to ace them. During the course of all those playthroughs, you'll almost certainly rack up all the other achievements without a problem. Of course, skill still plays a role, but only a handful of sections pose a challenge. For me, the hardest parts were beating the final boss on Dante Must Die mode and getting SSS on Mission 17. Apart from those roadblocks, persistence generally gets the job done.
(Devil May Cry achievements here)

Lego Lord of the Rings (Update: 2/11/13)

I was worried about this one. I played Lego Lord of the Rings for review, and nearly got to 100% completion. Because I was so close, I decided to keep playing after the review went up to hit the 1000 points. Unfortunately, I hit a bizarre glitch along the way that caused my treasure counter in the Tracking Hobbits level to be reset to zero. Basically, that meant that I wasn't awarded my final mithril brick for that level, which left me permanently one block short of being able to build all of the mithril items. Stuck at 99.2% completion with no way to fix the problem, I put the game down for a while. Yes, I was frustrated, but I had loved the game up to that point, so I was still happy with the time I spent with it. Fast forward to this morning: I asked myself "I wonder if they patched that glitch yet," so I dug out Lego Lord of the Rings and put it in. Sure enough, I get a patch notification, and just minutes later, I polish off the last few achievements. All in all, this was an easy 1000 points; it's less about skill and more about having the patience to collect every doo-dad. 
(Lego Lord of the Rings achievements here) 

Mass Effect 3 (Update: 4/24/12)

I wasn't sure if I was going to shoot for the full 1000 points in Mass Effect 3, even though I did for series' two installments. The game has a multiplayer-only achievement, which I normally have no interest in. However, I got completely hooked on ME 3's multiplayer mode, so a lot of achievements that would have required tons of single-player came naturally during the course of my online matches. Things like Pyromaniac (set 100 enemies on fire) and Overload Specialist (overload 100 shields) are easy to get with the waves of multiplayer enemies, and the ease of switching classes means that you don't need to do several full playthroughs of the campaign as different characters. As usual, beating the game on Insanity was the most challenging achievement, though I found it far more manageable than it was in Mass Effect 2. The only fight that really gave me trouble was the final duel with Kai Leng. I certainly died in other encounters, but none of them required nearly the number of retries as that one. The relative ease of the Insanity achievement has a lot to do with better design, but also with the weapon that comes with the From Ashes DLC, the particle rifle. It uses a cooldown system (like ME 1) rather than the limited ammunition of ME 2 and 3, so I didn't have to scrounge for thermal clips during the tough fights.
(Mass Effect 3 Achievements here)