Your web site has a purpose. Each page has a purpose. Everything should contribute to that. This is not to say that you can't have fun with things. Awards really don't belong on your home page.
Counters are another sticking point.
No one cares how many other people have been to your web site. If possible, get your access counts from your server's logs. If those aren't available, use a hidden counter, although remember that even those will require an additional internet connection, and will slow down the loading of your page. And then there are the people who collect animated gifs. These are incredibly distracting.