While it is not required that you search for conflicting trademarks, it can be a good idea to do so anyway. Should there be any existing trademarks registered that conflict with yours, your application will be denied, and your filing fees will not be refunded. Doing a little research ahead of time can save a headache later.
Additionally, it should be noted that because trademarks can be created through common law by using the mark, it is also advisable to search for common law trademarks. It is less important to conduct a common law search, but if you wish to, you should start with phone books, industrial directories, state trademark registers.
You can search for registered trademarks at the USPTO's website: http://www.uspto.gov/.
LegalZoom also offers a range of trademark searches that can fit your needs, whether you need to protect your logo design, brand or other identity establishing name.

