There's plenty of ways to remotely access or control a PC from Android, but LogMeIn Ignition scores highly for its slick approach and especially ease of use.
Remote access software is the kind of thing that you probably think you don't really need unless you're in some kind of dry IT management role. It's certainly got a place in those kinds of jobs, but equally, there's some definite appeal to being able to look up something on your home desktop while out and about, whether it's just checking details, sending yourself a file via email or scheduling a download.
LogMeIn Ignition isn't a free application, but it'll combine well with LogMeIn's free service and is trivially easy to install on any number of desktop machines, skipping the configuration problems that plague many other clients. [LogMeIn Ignition]