Office politics

Last week the boss called me over for a chat and took me by surprise.
A colleague had complained to the boss that I was being rude to him and I really didn't know what to say. Can you imagine me being rude to anyone in a professional setting, or even in general?
It started with a question - ``do you have any issues at the moment?''
``Nothing major'', was my reply.
I was then told that the guy who sits next to me had complained that I'd been rude to him for a couple of weeks. Well, I said that I hadn't. Though I said at times I didn't want to talk to the guy or was reluctant to pass on information that I had that he could know if he bothered to put in a bit of effort. Basically on that front I didn't want him to benefit from the time I put in (now to be clear we are talking about horse tipping and form and it is a matter of doing your own work there).
I was then forced to tell the boss that the guy had been baiting me at work, trying to get me to say things so that he could complain about me. Childish, or what!
Anyway, as much as I didn't want to bring that up just yet I had to and fortunately the boss said that he had noticed. So that appears to have stopped for the time being.
It left me pretty royally peeved about the situation and I didn't say an awful lot to the guy for a while and really only talk to him if I have to.
I realise in a work situation you can't give people the silent treatment for long and am going to have to push past it. It's hard though, I reckon I could go to the passive-aggressive Olympics if there was one.
This behaviour is not foreign to this guy, who seems to think he can control our workforce for his own gain and has pushed people out of their jobs in the past. I ain't moving and I think he realises that fact. What he doesn't realise I'd suggest is that I want his job/role and the boss knows it (I said as much about nine months ago).
The thing is, this guy expects people to respect him but he doesn't realise that respect is something that is earned, it doesn't come as a given.