You can do either. It depends on the level of security you want.
The OWASP Enterprise Security API (ESAPI) uses the single token per user session method. That is probably a pretty effective method assuming you have no XSS holes and you have reasonably short session timeouts. If you allow sessions to stay alive for days or weeks, then this is not a good approach.
Personally, I do not find it difficult to use a different token for each instance of each form. I store a structure in the user's session with key-value pairs. The key for each item is the ID of the form, the value is another structure that contain the token and an expiry date for that token. Typically I will only allow a token to live for 10-20 minutes, then it expires. For longer forms I may give it a long expiry time.
If you want to be able to support the same form in multiple browser tabs in the same session, then my method becomes a little trickery but could still be easily done by having unique form IDs.