When you don't show up to court in a civil case, the court can enter a judgment against you giving the creditor everything they asked for. Down the road, the creditor can ask that you be ordered to show up to testify about what your financial situation is. If you fail to show up to testify, you might be subject to arrest.
Not all creditors require you to show up to testify about your finances, so at this point, I am merely speculating about a future problem. Many times, the creditor knows where you work & where you bank.
The answer will depend on the state the case was files in as well as the service processor's reliability. A few years ago I would have said that there was generally no chance you'd go to jail over a debt, but recently there have been some people (at least one in Illinois) who had warrants out for their arrest for contempt of court for not providing documents they didn't know they were to provide. I happened to have blogged on this subject just this morning. There's a link to a recent news article within the blog itself.
I agree with the caution given in the other responses. This is the judicial trick-bag. While you cannot be arrested for not paying your debt, you can be arrested if you are ordered to appear in court and do not. So pay careful attention, if you are summoned to court-you must appear. Likewise, if the creditior gets a judgment against you, the Court may order you to appear at a subsequent hearing. If you do not appear, a warrant may be issued for your arrest for contempt of court. If you file bankruptcy, make sure the lawyer gets in contact with the court to make sure you are not held in contempt.