There are several reasons that you should filter your tap water. I think it is a good idea so that you actually drink it and avoid bottled water. We use a tap mounted model that works well in our area and takes out a lot of the chlorine. Some kitchen faucet systems have an undersink filter that can be installed. I found that system expensive and I couldn't gauge how long the filters would last. Using the filtered water in reusable water bottles has made carrying something to drink a lot easier and cheaper for us. Follow this link for information on filtering your tap water.
The odd thing about water is that we spend so much money on water and wastewater infrastructure to ensure we have a clean water supply yet millions drink bottled water.