The tags won't affect the pages directly by being on that page (although I am sure someone will say having the tag will increase your keyword density but I wouldn't even give too much thought to that). So adding tags in the hopes that they are directly a ranking factor would not be a good use of time.
How it can help SEO is when you have a dedicated page(s) for each tag that page will be naturally optimized for that keyword. That page will (theoretically) potentially rank well for it. That page can then drive traffic and potential link givers to pages tagged with that keyword. Also, the interlinkng by your pages will help to increase each page's PR as well as boost each other's rankings due to the advantages of anchor text and everything else incoming links have to offer. (Yes, internal links are very good to have. Just ask Wikipedia).