There are several browsers worth mentioning for viewing web pages. The two most widely used browsers are Internet Explorer and Mozilla Firefox. BBspot has a fun non-technical comparison of the two. There have even been several reports over which is more secure.
(As of 2005-08-19) Secunia is the home to security reports on over 5000 software products. Secunia lists 69 vulnerbilities for Internet Explorer (2 to 3 per month) from February 2003 to August 2005. Of the 69 IE vulnerabliities, 29 are unresolved. [18 are less than critical, 8 are moderate and 3 are critical] According to Secunia, Firefox has had 21 vulnerabilities (less than 2 per month) since it's release in August 2004. Of the 21 Firefox vulnerabliities, 4 are unresolved. [3 are less than critical, 1 is moderate]
There are two more intertwined factors to consider, usability and speed. Internet Explorer 6 and earlier require one window for each page you open. Also, many random scripts or pages can cause Internet Explorer to crash, due to IE's failure to meet web standards, losing all open windows and usually the history of those pages. Firefox on the other hand can open all pages in one window via tabs, similar to most spreadsheets applications. Tabs in a single window require far less memory than multiple windows, meaning that Firefox should run faster and crash less on most machines. Firefox crashes are reportedly much less frequent, and typically with no loss to history. Some Firefox extensions allow the browser to reopen with the tabs that were open prior to closing or crashing.
When it comes to the internet, speed is always better. Usability is a nice bonus. Security is essential.