This was probably great in 2004, quite easy to breeze through.
The story it's pretty good, but I can't say it's heavily based on the "Godfather" movie, but I don't see how they could go in a different rout. You play as Jimmy, that progresses from an ordinary Taxi driver to a Mafioso type. The pace of the game is good an the characters will make you care about them. I really like the way the game ends, it's a good story and they tried to be very cinematic on the game structure.
The game is pretty similar to GTA, you drive around from place to place, fulfill the missions that they give you and so forth. The only side mission that you can do it's all based on stealing cars, which get's pretty tedious after a while, it's the same formula and I stopped caring after a while. The driving it's so so, I guess it's about accurate since you're driving early on cars, they handle quite badly. The shooting is also a little touchy, I got until the end of the game thinking the aiming sucks, it was pretty sensitive and it will go wild with a little touch on the directional pad. The simple secret to fix this, just go to the settings and set the sensitivity to low, it made miracles for me and I quite enjoy playing after this.
I have to say that I found this game quite easy, the challenging stage for me was the final one, it took me a few hours to figure how to progress.
I enjoyed the game for what it is and for having played on 2011 since I want to get to Mafia 2. Today it might feel very bland and old school but you can have a good time playing it.