If you frequently download files from suspicious sites, it's probably worth it to check for viruses Before you download, instead of waiting to see if your regular anti-virus software will catch it after you download.
The solution? You can use the Dr.Web plugin, which will add an item to the right-click menu to allow you to scan any web page or download link using their online virus checker.
Let's take it for a test drive… I decided to scan the Dr.Web Firefox plugin with Dr.Web, just to see what it would say.
Looks like it's clean! (shocker)
Keep in mind that no anti-virus software is absolutely perfect or will catch every virus, so this isn't a substitute for using a proper anti-virus software. You should also still be careful where you download files from.
This plugin will also not work for webmail attachments. I tested this on Gmail and it didn't work, which isn't necessarily a bad thing, because it means your attachments are private.
Firefox
Download Dr.Web Anti-Virus Link Checker from Mozilla Add-ons
Internet Explorer
Download Registry Hack for Dr. Web Anti-Virus Link Checker
Opera
Instructions for adding a context menu item to the Opera browser.