Double Click on My Computer (I'm assuming you're on XP), then click on Tools from the menu and select Folder Options. In the Folder Options window that opens, click on the File Types tab. Scroll down and see whether HTM and HTML file types are associated with Internet Explorer. If not, click on HTM, then click Change below. Scroll through the list of programs and find Internet Explorer. Then do the same for HTML.

You might also check your system for spyware. Do you have current Antivirus and Antispyware software installed?