You use counters to see how many people visit your site. Some counters also offer statistics, but I don't think personal non-commercial sites need these features.
You can get free counters from:

• BoingDragon Web Counters
  This site offers very unique counters. The counters are animated characters, like a wolf, a dragon, a fairy etc.
• The Ultimate Counter
  This site offers a great variety of fonts and styles for your counter. It also offers clocks.
• Le Fast Counter
  Very simple counters. You can choose between a few colors. But they do the job just fine.
• AADDZZ counters
• BeeSee.Com Hit Counters
  A few simple and nice styles to choose from.
• Many "free homepage" providers (like Tripod, Geocities) also offer counters.