I use Konqueror most of the time. It seems to work fast, and it doesn't have those crappy fonts that Netscape 4.72 has. I also sometimes use Mozilla, although I prefer Konqueror because I find Mozilla to be a little slow. The only problems that I have with Konqueror are that sometimes when I do a search on a WWW site I don't get back any results, instead I just get 'File. Unspecified Error' but maybe that is the fault of the WWW site I am searching at.
The other, more serious, problem with Konqueror that I've come across is that it causes my system to slow to a crawl in certain situations. I was at the Infoseek.com WWW site trying to do a WWW search. I clicked on the 'Search within these results' button and my whole computer slowed to the speed of molasses. My harddrive light lit up, etc. I had to reboot it. I'm not sure why it did this, but this only seems to happen when I'm doing a search at Infoseek using Konqueror. Weird.

Other than that I like Konqueror though.