I really want to play Mass Effect 2. I can't remember another game that has gotten as much widespread acclaim as ME2 (then again, I've only been following game journalism since about 2007). 
 
The problem is, I haven't played Mass Effect 1. 
 
My backlog is full of Christmas games (BC2, Fable III, Sims 3) plus some others that I have laying around (AC:Brotherhood, New Vegas).  I'm not sure that I have time to play through two 25+ hour games, although if it's recommended, I will.  
 
So, will I still enjoy Mass Effect 2 if I haven't played the first? Or should I definitely play through the first game prior to indulging in the second?

I think you'll get more out of it if you played one. There is a huge amount of story in there that you need. The gameplay is different enough that you won't need to play the first to grasp it, but what you'll miss out of if you don't play will leave you with a far less rich experience.

I think you will still enjoy it, just not as much as you normally would. Most of the characters in your party are completely new people, so you aren't missing anything with them. However, some of the backstory and some of the other characters will have a history of sorts that you won't get to see. You can beat the first game in ~9 hours if you power through the story, so I would suggest doing that. Don't bother with too much side stuff.

Mass Effect 1 is still an amazing game, I played through it five times and got achievements, I would play through it again if I didn't have other games to play
 
Mass Effect is a better game then all those you mentioned, well atleast in my opinion

I think so, it's still an immensely entertaining game on all levels. 
 
But,
 
You won't have the knowledge of the world and it's characters (mostly the world), which is key to getting the complete experience, and the fact that you won't have a save to import is also quite a bummer. If you are up for it you should definitely go and play the first Mass Effect, even though it is rather clunky and outdated. 
 
I am sure that you'll see the qualities of ME2 even if you decide not to play ME. 
 
My advice is to play the first game, it will give you a much improved and customized experience with the second game. 

Yea you can, my friend only played 2 and he loved it.  Honestly the key parts of ME1 are well summarized at the game's start.  But if your interested in the franchise ME1 is still worth a playthrough, you can get both games pretty cheap now.

You'll really want to play the first game. You can go ahead and just play the second, but it doesn't really make much sense to do so. A lot of the appeal of the Mass Effect series is a continuous narrative that follows your specific character across all three games. Skipping a game misses a vital part of the experience and it will also mean you won't understand quite a number of things that happen during the game.

 You don't need to play first one, but it's a good idea if you do.  It's a fine game, and there's so many damn winks and nods to actions you took in your ME1 playthrough while playing ME2 that I'm guessing you'd just miss out on.  
 
Also, I don't think it's a bad idea to set aside Fable 3 and the Sims 3 for ME1 & 2..    

whoever is telling you that you'd still enjoy it is wrong 
 
its part of a trilogy. which means each installment is equally important for.. everything.  you must play the first.. if its any consolation, i was in your shoes 2 months ago, and i beat ME and ME2 during November/December, while progressing in 10 other games.. so you'll manage !

Go ahead and play 2. You'll be fine.
 
! has a great story, but it's a little rough about the edges. It all depends on how much spare time you have.
 
It's not a life or death issue. Catch up on ME1 on Youtube, and plough into 2 at will. You'll still have a blast.

"whoever is telling you that you'd still enjoy it is wrong "

I'm also in the shoes of do I play ME1 or just jump into ME2. How long is the first one just out of interest?

" @Ahmad_Metallic said:

"whoever is telling you that you'd still enjoy it is wrong "

I don't agree. Sure, you'll enjoy ME2 infinitely more after having played ME1, but the designers of ME2 were very clear on the fact that they wanted the game to appeal to new audiences as well as those already established (much to the dismay of many of us on the BioWare forums).It still offers the deep codex that can fill you in on a lot of things. You can create a new Shepard from scratch. It still offers compelling gameplay even without knowledge of the story hooks from ME1.  That said, of course I'm of the opinion that people should play both games. "

There isn't anything in the first game that is essential to understanding the story of the second. Many of the events that seemed important in Mass Effect were trivialized in Mass Effect 2. Overall, it's a completely new plot with very thin connections to the first game. In any case, I would strongly recommend playing the first Mass Effect game, if only because its story is far superior to the story in Mass Effect 2.

Playing 1 really enriches the experience of 2, you can plow through the original game in about 10 hours if you're in a rush.

Play the first game. Who knows? You could be in the percentage of gamers who love it more than the second, like myself.

You'll get a much fuller, richer experience if you play 1, but if you haven't it's kind of like leaving the toppings off a sundae. They're nice to have, but at the end of the day you've still got a dish full of ice cream. And that ain't bad.

Nope

Play the first one first.  

Play Mass Effect 1. It's worth your time to ignore the other games in your backlog. Trust me.

" Play the first game. Who knows? You could be in the percentage of gamers who love it more than the second, like myself. "

if you decide to play Mass Effect 2 without playing the first game you will spoil the best parts of ME1 and won't have such a great experience as you would get when you play it in the correct order. Mass Effect 1 is still one of the 10 best games on the 360 in my opinion so you shouldn't miss out on that experience plus it's pretty cheap by now and easy to get through quickly if you really want to. You won't regret missing out on Fable 3 or Sims 3 instead, trust me :-)

I always recommend playing the first one due to how much it sets up and how your story continues in part 2.  I also prefer the main story in the first one, by a considerable margin, actually.
 
But I always add a "but" in there.  The gameplay just isn't as tight as the second, and might really kill your interest in the franchise.  Seems extreme, but I've seen it happen to some people.  It's not bad, but it doesn't measure up to pure third person shooters at all.  So I guess you should limit your expectations on that front.
 
You can go into ME 2 without playing the first, although you'll get a lot more out of it with ME 1 in the bag.