Clearing your browsers history periodically is a great way to maintain a healthy browser. The more you use your browser the more information it "saves", over time you may run into issues like logging into websites.
It is a good idea to clear your browser history every now and then.
You can start by going to this site. Click on your respective browser and get specific instructions on how to clear your history.
There are also some free utilities that can do this in addition to a lot of other things to help your browser. One of those utilities is CCleaner. It can clear your browsing history as well as your cache. Instructions on how to use it can be found here.