You shouldn't play ME2 without playing the first one. Not because you'd be totally lost, having no idea what's going on (it's a video game, the story isn't that complicated. I could give you a good run-down in a couple paragraphs, and you can go through the codex in-game for details), but just because the first game is good too. It's not like it's a bad game that you have to slog through in order to enjoy the second one. The first one's great! Not to mention cheap. You should definitely buy and play that one first.

If you do have some strange, obscure reason for not wanting to play the first one though, then yeah, go for it: play Mass Effect 2. The reunions and nostalgia of old friends won't affect you much, but you'll pick up the story and general gist of things with no trouble at all.

tl;dr: Play ME1 first. If you can't or for some reason won't do that, then yes, you should still get ME2. Definitely.