Spyware can collect anything from a list of internet sites you visit, to password information or act as a keystroke logger.
Adware can do what you suggest. Sometimes it just popups up ads randomly when you're not even online.
There are browser hijackers that redirect your start page to theirs, or worse. 'Search toolbars' that load into your system and hijack you to their page. Our lab is infested with malware so badly, some of the machines won't allow the administrator account its priveleges.
I believe these things exist, I just think they have to be things that are related to, or come with stuff they are installing.... Things like Gator, which comes with Kazaa... it told me a little fib about what it was, and I said OK to install it. It was there because I let it in. Since then I am very wary of installing anything that is freeware or the like, and coincidentally, I've been clean.
In other words, I don't see how they come in without cooperation, or I'd have it too. ecurbh is more adventurous than me, and is also clean.
You don't think it's possible, that there's a correlation between spyware and freeware?