Tell him you aren't interested in the conversation. Politely, but repeatedly if need be.
Ignoring him, or giving him generic nods of confirmation and token acknowledgement, are only going to feed into your co-worker's desire to gossip and complain. State clearly and plainly that you are not interested in hearing about this gossip. Point out that you would like to get back to work, or continue to eat lunch, or whatever you are doing at the time that you would rather be doing when he tries to engage you in conversation.
Be Polite though, no matter what. He is your co-worker, and you have to work with him even if he is being a bother.
If it starts to interfere with your workflow, and he refuses to stop, consult your supervisor in private. Explain that the constant distractions are getting in the way of work (don't bring up the conversation topic - that's irrelevant) and ask to be assigned to a different seat.