Is this a good gaming computer, and can it play most games well?

the 3 ghz processor sounds great and should prove to be very good, 4gb ram is quite a bit and should be good, usually the minimum is 2gb ram. 21" monitor would be like playing on a small hdtv, so that would be good. 1gb graphics card is awesome and your games should be in great detail and that detail will be at its maximum thanks to your full hd monitor. 1tb hard drive is a must with a gaming computer as it means you can install alot of games, as well as hold alot of save data such as photos and doents. the mouse will be great, the dvd drive is good but would only be useful for playing dvds or burning them. sound card is good and so are the speakers so if you are playing a first person shooter, sound quality like guns should be good, however there are better sound systems out there. warranty is good because if you are a gamer you will be constantly using it. great cooling system is needed due to your powerful processor, data backup is good if you dont want to lose your saved games and if you store alot of photos. works isnt necessary with gaming but normally comes pre-installed and can be removed. your anti-virus only lasts 15 months after that i would reccomend AVG