Firefox 3.0 is much more efficient when it comes to memory when compared to other major browsers. This is according to testing done by independent tester Sam Allen.
Sam Allen wrote a memory-monitoring utility, by the name of Memory Watcher, to track usage by Firefox 3.0, Opera 9.5, Flock 1.2.2, Safari 3.1.2 and Internet Explorer 8.0.
The testing wasn't done in a scientific manner, but still should be able to give a reasonable idea. Testing was only done with Windows versions for each browser.
According to Sam Allen, Firefox 3.0 was the winner because it used the least amount of memory, its memory use didn't noticeably grow over time and it releases memory to the system.
Safari 3.1.2 for Windows. Allen said it consistently consumed more memory the longer it was used and showed extremely poor memory management.
You can see the complete report and test results here
Firefox 3 Memory Benchmarks and Comparison