The only real function of a robots.txt file is to keep robots out of part of your web site. If there is no area of the site which you want to keep unspidered you have no real need for one.
A very minor advantage of having an empty robots.txt file (which bans nothing) is that it will keep some "error" messages out of your logs. Every time a robot visits your site it asks for the robots.txt file. If there is none the robot will get a 404 error, which will show in your logs.