At the time of writing there were about 16 million organic compounds known. How many more are possible? There is no limit (except the number of atoms in the universe). Imagine you’ve just made the longest hydrocarbon ever made—you just have to add another carbon atom and you’ve made another. This process can go on with any type of compound ad infinitum.
I got this from Organic Chemistry (Clayden, Greeves, Warren, Wothers)...
I don't really think that there's a site with "all" the organic compunds structures known... anyway you could try a professional app such as ChemDraw Ultra which has a huge database and can also connect to other DBs on the net. Even Mathematica has got a database (retreivable from the net) of molecular structures and data. They're both commercial apps but if you really need them you could decide to invest in them (maybe in ChemDraw, which is more specific and cheaper too).