If you are a day trader, the computer you use could be the difference between making money on a trade and losing money on a trade. The quicker you can enter and exit trades, the less potential for slippage there is. The markets move fast and so you need a fast computer to compete. If you can afford it, the computer you use for trading should only be used for trading. (If you can't afford a computer dedicated solely to trading, you should allocate a portion of your trading profits to buying a computer used just for trading.) What this means is that you should not let your spouse, children or friends use your trading computer for anything. You should also not use the computer to download anything other than your trading platform from the internet as spyware and malware will slow down the performance of your computer.
The specs of your trading computer should be based on the trading platform you will be running. It is recommended that you buy as much computer as you can afford and not just to meet the minimum requirements of your trading platform. For example, a trader using TradeStation 8.1 finds that a using a Dell Precision Workstation 470 with a 2.8 Ghz Xeon Processor and 1.5 GB of SDRAM is sufficient for his needs. Note that this is a pretty powerful system. The best way to find out how to configure your computer is to call technical support of the trading platform you will be running and ask them for a suggestion. No matter what, it is recommended that you buy a computer that can support at least 2 monitors.
For a swing or long term trader, the speed of your computer will not be as important due to your longer time frame. The speed of the computer will be important for your back testing but is not as critical as presumably you could be doing something else while your computer is testing a strategy.