My favorite and default are apparently Mozilla. I would like to view my work in progress with several browsers (and different resolutions, if possible)

Is this a question? Well, if you design websites than you actually "need" to be able to view them within the different browswers. The only way to do this is to download and install each browser on your computer.

Just adding my 2 cents here,
DianeD

I'll assume you want to know aobut which browsers to use:

1) Firefox/Mozilla
2) Netscape
3) Opera
4) IE

Listed in order of importance. 99% of the time if it's right in FF then it'll be right in IE due to IE's support of little imperfections vs. FF's inability to deal with anythign that is'nt strict W3C standard

This had been addressed before, there are some web-sites out there that will test your page for you, but you need to have web-hosting already in place to use most of them.

I primarily test in Firefox and Internet Explorer (as they are the most popular browsers).

http://www.browsercam.com/ seems to be a popular one (but you have to pay after the 24 hour trial is up).

I'd also add Safari to the list of browsers to test for and it's also advisable to test in something like lynx or another non graphical browser.

I develop in Firefox and then tweak things for IE, but given the overwhelming use of IE it's going to be the most important broswer to test for the general public.