One of the simplest types of products would be a two-asset cash-or-nothing option. You can read about pricing these in the Collector's excellent guide to option pricing formulas. While the overwhelming majority of these trades are proper OTC exotics, some particular flavors have been getting increasingly more vanilla. In the world of rates, for instance, you have CMS spread options, which offer exposure to, among other things, correlation between different points on a yield curve. As I understand it (and I am not an expert), in energy-land crack spread options offer an example of an implicit correlation trade.
the trader was the head of the trading desk at the same time that was a subdivision of the bank (brokerage), it was in the nineties. The bank had bought the brokerage cause they had no real experience in trading. So the trader also overlooked everything. The trader had allready cashed in when the broker was taken over as the management used to be partly owner too, guess he saw the whole thing as an extra option for him personally. I know it sounds like a joke, but it happened ... I know an even worse story of a desk where an option trader (the guy has died of cancer in the meantime) that hid his position from a bank where he valued his index options at vol 18 where in reality the index was trading over 30. Only two other options traders knew this, risk management knew nothing. I found this out by accident as I happened to visit that trading desk and had seen something was totally wrong with the greeks of the position. One of the other options trader I knew signed me to shut up. He later told me on his private phone how it really was. As vol later in the year took a dive he managed to get away with it. This was at another bank.
urgh, check out autospreader.wordpress.com in a day or so; I will toss up a few correlation related posts this weekend for you that I have been holding off on. This (correlation trading) is a rocky road to tread considering you only are looking at a very small part of the overall picture. It is in practice many times that you can't correctly abstract the risks away involved with products to trade only correlation and you will be stuck holding a basket of much riskier crap. Google dispersion trading, variance swaps, and correlation swaps.....familiarize yourself well they will be your friends. On a much smaller scale, there is something that you can do between treasuries and eurodollars (cash - futures) to trade the correlation.