Bad sectors are caused by physical damage (dropping the HDD), wear and tear over time (the disk gets old and stops working), or they can be as a result from the manufacturing process (all disks have bad sectors from the factory).
You will start to see bad sectors if your data on your disk starts to corrupt, e.g. your PC does not boot correctly, video files no longer play etc. You may also notice a decrease in disk IO performance.
To do a simple test, download and install speedfan http://www.almico.com/speedfan.php. Select the SMART tab and see if there are any errors, especially reallocation errors, which are bad sectors that have been moved to good sectors and marked as unusable . SMART is probably one of the best indications of a faulty disk...
For bad sectors look at the Reallocated Sector Count, it should register as OK. If any of the attributes are not OK, or blank (the vendor does not see the attributes as important), then a disk failure could be immanent.