Whilst Nike are known for producing a lot of thick sneaker models in the last decade, some of their classic are still very popular. The Nike Blazer is one model that has stood the test of time, offering simplicity, yet versatility in styling.
If you're looking for a thin sneaker, this might fill the bill. On the outside it might be deceptively thick, but in reality these are well under an inch. I measured a brand new pair of Blazer Low's as giving you 1.7cm, or about 2/3rds of an inch. With a few months of wear, I expect them to settle towards a solid half inch range.