If you pretend to spam all over the internet just to get backlinks to your site then the answer is 0.
Now, when these backlinks are real and done for the right purpose, then there's never too many.
What do I mean with this?
In the first case, if you dedicate your time posting in blogs or forums which may allow you to post a signature or link to the site you want to promote, and you simply post for this purpose of having links to your site, then you'd rather dedicate that time to something else. It is simply not productive and, even if you may think otherwise, you'll be spamming. And it would useless. Search Engines already know that it is you who adds that link and that you're doing it for the wrong purpose and then ignore it.
In addition to that, the webmaster of that site may have those links as no-follow, making the value of those links even less (and their value was nothing, anyway)
In the second case, if bloggers and other webmasters write articles and link to your site... that does have a lot value as it would mean that you have great content. You want as many of those as you can get and as to many articles as possible.