"Untouched" by you, maybe...
Whether you've got dial up or DSL ("always on"), you always ought to disconnect from the internet before you go to be, AND have your connection set so that it can't automatically reconnect.
In addition to people using your computer remotely, planting bugs, or perusing your system for info, spyware & malware doesn't operate like normal ask-your-permission-first cookies. Its job is to sneak onto your system, then report back regularly. That's the main reason your system slows down so much- you've essentially got a whole bunch of other people using your internet phone line at the same time you are. Also, just like hitting "refresh" when you're offline will automatically reconnect you (with some connection settings), a great deal of spy & malware accomplishes the same when it tries to "refresh" its contact with its home-base.
In the end, it's just a good idea not to leave your computer online overnight OR disconnected (you think) but with your connection settings in "automatically reconnect" mode. The spy & malware is obnoxious enough, but there's worse out there. In particular, the new corporate security systems don't just kill viruses, they try to hunt down the hacker and fry their systems. Since a standard hacker practice is to hide themselves by routing their stuff through a series of innocent people like you whose computers are online, that means that you're potentially in danger of having your computer fried by Microsoft, Sony, or one of the other companies that use one of the new aggressive security programs.
Fun, huh?