I'm looking for a good set of speakers (or a setup) that will run me under $200 USD. I want something that has ill sound quality even when really loud and something that can blow the bose companion 3 speakers and sub out of the water. Any suggestions? I'm open to buying an amp and w/e else is needed as long as it runs me under my budget. Also I will be using these with my iMac, iPod Touch 2G, Lenovo Thinkpad and hopefully iPhone 4. 
 
Any suggestions would be appreciated. Thanks

Hi I would recommend active monitors , you can get some decent ones for around 200 used, In general you'll  get much better sound quality from an active set rather than a separate speaker/amp setup, and yes they will blow the bose companion 3 out of the water I have some event Tr6 active speakers which sound better than many much higher priced speaker/amp setups I've heard. If you want to go the separate amp/speaker route you can check out some single driver speakers like  tekton design speakers but these do lack bass sometimes.

What active monitors should I try for then? Which ones will fit nicely on a desk? Also, do they have a nice base?

I would go to a guitar center and try out the ones they have, they have room with only monitors and you can hear each one. its good to do this because that way you know if the monitor has enough bass for you, find a few models you like and see if you can find them used. The last time I went there some JBL's I liked whcih were like 400 but I forgot the model name. I'm currently upgrading my speaker set-up and I'm selling my event tr6's over at the for sale section here incase you or anyone else is interested.