Here are a few things that will get you in trouble:
Gaming the reputation system.
You can't make more than one MSE account and have your accounts shower upvotes upon each other to gain reputation. Similarly, you can't make a deal with another user to shower upvotes upon one another to gain reputation. (So, don't give all your upvotes to just a couple people, as we won't be able to tell the difference.) Conversely, don't downvote another user into oblivion out of revenge if he somehow makes you mad.
Abusing other users.
MSE is a professional environment, and as such everybody is expected to be behave in a reasonably professional manner, which includes being nice to one another. Suspensions in this area most commonly stem from repeatedly hating on new users, developing a vendetta against a single user, or having a persistent negative attitude that detracts from others' ability to enjoy the site. It's easy to be mean on the internet, but MSE is not a good place to take out one's frustrations.
Asking bad questions repeatedly.
Bad questions are defined loosely by the What Not to Ask section in our help center. If you're not getting lots of downvotes and negative feedback on the questions you ask, you don't have to worry about getting suspended (though users should always endeavor to improve the quality of their posts). Also, don't ask the same question over and over, even if you delete the older copies.
There are a few other reasons for suspensions, as mentioned in the comments, but these are the most common. A general rule of thumb is to strive to be helpful, honest, and cooperative with the rest of the community; this should keep you out of the moderators' crosshairs.