Pick of the Best
Perhaps the best first download is Fritz 5.32. This is a top-notch, fully featured chess playing program. When combined with Chessbase Light 2009, you probably already have enough chess software for playing against the computer, analysis, and all sorts of database study.
But why stop there when there is so much more! The only shortcoming of the above combination is that it doesn't allow you to use one of the many free chess engines available on the net. SCID and Chess Assistant 7 light both support the UCI protocol and its many engines, and so are a good alternative. Using SCID you also don't have to worry about the database size limitations of the light versions.
Of the engines, for strength, Rybka is second to none, and the free version would be favourite against any world champion! Another strong engine for analysis is the open-source Toga, whilst Pro Deo is many people's favourite for it's human-like play and personalities.
But the best opponent is always going to be a human. And using the internet, you can play with someone on the other side of the planet as easily as if they were in the same room! An excellent interface for this is Babaschess.