You can certainly go overboard looking for forums and blogs that can give you dofollow links back to your site. Still, it is useful to know this information.
This used to be very easy a while ago if you had Mozilla Firefox, since you could just mouse over a link on a page, scroll down to "Properties" and it would tell you. This particular facility seems to be gone from the more recent versions of that browser. Or at least it's not so easy to access.
That said, you can still download a nifty add-on called NoDoFollow which highlights the different kinds of links with different colours.
Also, there are various free detector tools that will tell you what kind of links a page has when you type in the URL. Here's an example.