Yes, that wouldn't be great for SEO because many of the pages will be almost identical and there are almost infinite combinations. It is akin to a generic search page, which Google discourages the indexing of.
There is nothing wrong with the pages existing, if they are useful to users. You can simply block search engines indexing those pages - probably the best solution would be to add a meta tag to those pages:
<meta name="robots" content="noindex,follow">
This will prevent pages being indexed, but allow search engines to visit and spider the rest of your site. Using a robots.txt file is another option if the above isn't possible.
Having said the above, individual tag pages (as on Pro Webmasters, Stack Overflow, etc) would be pretty useful as they are much more finite and split your content into clear categories. So if possible, do not block those pages, only the tag combos.