Cease and Desist & Minimal Fees
When you receive a copyright infringement notice, usually the copyright holder will simply ask you to "cease and desist" use of the copyright. Most terms of a cease and desist letter are usually reasonable. For example, Getty Images has a policy of only seeking to be put in the position they would have been in had the image been properly obtained (in short, they're only looking for the licensing fees that should have originally been paid to use the image for a particular period of time).
Litigation & Statutory Damages
If you have encountered a copyright holder that is looking to engage in litigation against you over the copyright infringement (or if you have repeatedly failed to answer a copyright infringement notice letter and/or cease and desist use of the copyrighted work), then your situation can escalate dramatically.
Generally, litigation will lead to statutory damages.
Under United States federal copyright law, a copyright owner can be entitled to damages between $750 and $30,000 per infringement. If the copyright owner is able to show that the infringement is willful, the law will allow them to seek as much as $150,000 per infringement.
The modern trend doesn't give any slack to copyright infringers - recent jury awards have ranged from $675,000 - $1,000,000. A jury in Western Washington state awarded a copyright holder over one-million dollars in damages for the unauthorized use of 5 images.
The key here is to not panic. The cost of a copyright holder engaging in litigation is extremely high (think 6-figures), so the odds of someone wanting to take a copyright infringement suit to a jury is low. This is because they don't want to take the risk of losing. However, you should still try and respond to the copyright infringement notice in a timely manner.