When I heard about the series, I initially dismissed it as being a big budget shooter in the same vein as CoD or Halo, with lots of action and shooting and little else. (No offense to CoD fans, of course; just not my type of game.) I started the first one a couple times and never got into it. Recently, however, I picked it up again, and played through the whole trilogy. Ironically, the shooting in the first game is a little clunky, making it not a very good shooter game at all. (This is vastly improved in the second and third installments.) What really got me, though, was that it was a role playing game with actual roleplaying! You decide how your character plays out, your actions influence his/her personality, and your decisions make a massive impact on the game universe - even two games later! (Your character and save data, including the decisions that you make, are carried from game to game.) I love that you can fail an objective, and rather than getting a "Game Over" screen, the game keeps going with the story continuing as if Commander Shepard really failed that objective, and the consequences of that failure now being a plot point. The game universe and characters are all incredible and likeable - I especially came to love each squadmate that joins you over the course of the game. (Even Jack, whom I initially found incredibly distasteful.) The different alien races are unique and engaging, and the depth of backstory put into everything is impressive and worth reading.
Anyway, just thought I'd throw a recommendation out there. I sometimes crawl over this board when looking for new games to play, and I want to throw this series out there as one of my new favorites. This series gets my official stamp of approval. If you haven't yet, give it a try.
Also, on one final note, there are a couple of mods out there that I recommend as well, both of which are for the third game: the MEHEM mod, which improves the ending significantly (if you haven't played the games yet, don't read up on it or it will spoil the ending for you - just take my word for it and install it,) and the Citadel Epilogue mod. (As much as I dislike paid DLC, this mod ties in with the other one to really make the most of the content in tying together the final emotional strings. It costs $15 extra since it requires you to have a piece of paid DLC installed, but it's worth it, in my opinion.)
Finally, there is also a high-res texture pack out there for ME1, which makes it look a little less dated, though it has still held up pretty well.