If you are only a Tor client (e.g. you're using Tor Browser to browse the web), you are not an exit node, or any node at all, and you are fine. Nobody will be able to tell where your traffic is going, except of course the exit node. Granted, some exit nodes might do some shady things, so HTTPS over Tor is your best option for maximum security and privacy.
If you're actively running a Tor node (i.e. you're listed as a possible route by the Tor directory authorities), that's different from just being a user. You can't be a node by accident; you have to set some stuff up. If you're not an exit node, then everything that goes through your server is encrypted, and no web service is going to know you were even involved.
If you're an exit node, then web services know traffic is going through you. Then you could get into a little trouble. The most notable thing that will happen is that you will be deluged in DMCA notices. Fortunately, that's not your fault, and Tor prepared a response letter for you. Your ISP might not be alright with you running an exit node (or any kind of proxy), and some might just disconnect you. There is a list of good and bad ISPs in this regard. Because of that, and because of warrant/seizure laws, running an exit node from your home computer(s) is almost certainly a bad idea. You'll also run into legal problems if you snoop on the outgoing traffic, but hopefully you're a good guy and aren't doing that anyway. Further reading: Legal FAQ for relay operators.
In summary, Bad ThingsTM will probably only happen if you're explicitly set up as an exit node, and even so, you'll probably be alright if you take the appropriate precautions as outlined in Tor documentation. If you don't run an exit node, you're good.