As a complement to Adam N. the ESMA (the EU market regolatory body) is providing its huge open database of financial instruments (all sorts, with 6 million derivatives or so), called firds, free of charge. You can consult it online and download the whole database or its updates.
You can see an example (the first column is the ISIN):
The limitation is that these are products traded in Europe; but it so happens that a good chunk of non-European instruments are traded on European venues, anyway so there are chances that ESMA knows about them.
For your information, the download files are classified according to the CFI classes. For derivatives: F for futures, S Swaps, O for options, etc. This is a massive amount of data in XML format, so if you are willing to use them, be prepared!