Do wallet stealing viruses exist? After I install the bitcoin client, what are the risks of browsing the Internet? Can my wallet be stolen?

Are there any known viruses/websites etc....?
Money can now be stored in a single file inside your hard drive. This is a natural target for criminals so yes, there are virus that steal bitcoins.

If you trust a third party (like an ewallet) to hold your coins, you will not have to worry about wallet stealing virus nor about wallet security. Instead, you should protect your login credentials and/or use a two-factor authentication mechanism. Treat your e-wallet account the same way you treat your e-banking account.

I don't know of any dangerous websites, but there was a report of a bitcoin trojan by Symantec on June 2011.