Nike Air Max 200 is one of the more recent models in Nike's long-running 'Air Max' series. It contains a more sophisticated air unit providing suprisingly good bounce when walking.
In terms of how thick the 200's are, I measured a brand new pair provide you with a very decent boost, in the 1.5 inch range (3.9cm). With most sneakers, after some wear they will lose a couple of mm.