Keylogger software to get your passwords (or whatever else you type).
Pop up software to have pop up ads (usually porn) show up even when you're not opening a website that has pop ups (they just connect to your computer through your Internet connection). They figure that if they do this on enough computers, a certain percentage of them will click on the ad and make the hacker some money.
They can cause registry problems (usually just a side effect of the bad software they put on your computer by fooling you into downloading something).
There's more, but that's the majority of what's done.