As others on this board have said, this game is an absolute must get.
A testament to its greatness is that I still think about it's story having finished it almost a year ago. For me, a game will engross me if I feel the characters in the story have some substance, and the story itself actually has coherence and themes. Mafia has all of this; a great cast, a great premise, a great climax and a memorable ending.
Comparisons with GTA 3 are inevitable. On the one had, I reject the comparisons because the games have more similarities than differences. While Mafia is more mature, GTA 3 is probably more adept at providing a quick action fix. Mafia's car physics are more mature; it's storyline is more mature and has more substance; it's combat is much more refined; it's graphics are more realistic.
Clearly, on the other hand I invite comparisons with GTA 3 because Mafia wins on almost every level, and that's saying a lot because I had plenty of fun with GTA.
Just buy the game, play through the first few missions and before long you won't be able to put it down. It's probably in my top 5 all time PC games.