The gold standard in encoding mp3's is LAME (as mentioned above for Goldwave). However, to get a good sounding mp3 you have to use lame correctly. It is commandline software but there is a frontend (GUI) for it called Razorlame where setting up the options are very easy. You can find it here:
http://www.dors.de/razorlame/download.php
Once you have this, for typical uses use the following settings once you have razorlame installed:
1. There will be a button on the toolbar labelled Lame, click it to open the lame options.
2. Click the Expert tab and check the box "Only use custom options".
3. In the "Custom options" box type exactly (but with no quotes) "--alt-preset standard".
4. There are only 2 other options for you to think about, under the General tab, you can choose where the file will be saved, I typically have it go in the "Same as input directory" and under the Advanced tab, there is the option to Delete source file after encoding which will delete your original .wav after a successful mp3 file is written. These choices are up to you.
Then just drag and drop your .wav files into the box and hit encode or you can add the .wav file from Add Files button and hit encode, its your choice.
Using this method will give you a great sounding .mp3 as quickly as possible. I am very particular about my music and have converted hundreds of CD's to mp3, and before doing so investigated all of the options on audio forums. This is the preferred method to use.
Let me know if you need any additional assistance.