
I have seen the above dialogue box twice in the last week and it just creeps me out.
I cant think of any good legitimate reason a Website should have access to my local clipboard.
After doing some reading on this apparently IE7 can sometimes set this off in error and you can turn it off, however I would rather be bothered with false positives than not know what a particular Website is doing to my computer.
There are a number of Websites on the web designed specifically to try install Malware/Spyware on your computer or worse steal confidential information like usernames and passwords.
The number of these sites is growing.
In the bad old days Viruses\Malware\Spyware travelled by e-mail but in 2008 you are more likely to get hit by visiting a Website.
Tip: If you have any doubts about a particular Website, exercise caution move on and try another one.
Things to Avoid: Sites that try and install software.

The above prompt is trying to install an ActiveX Control. An ActiveX Control is like software that installs in your web browser.
Tip: In some cases you may need to install an ActiveX control to access some feature of the site but only accept those you *REALLY* need. Clicking yes blindly to everything is asking for trouble.
On the link below is a well written but slightly old article on Malware.
Link: http://arstechnica.com/articles/paedia/malware.ars/1