The popular autosomal (aka "cousin finder") DNA tests are still a new science. Some folks still seem to be skeptical of the results and their accuracy. For sure, I have a ton more matches with unknown common ancestors than I do ones with known common ancestors. But in general, I'm optimistic about my overall match list (1,003 at 23andMe, 290 at ftDNA).
In general, a "real" match shares at least a 5 centiMorgan segment (or 7cM; depends who you're talking to). That doesn't mean that matches with less DNA aren't real, just that they might not be... Our DNA recombinants; it mixes up. The smaller cM segments might just be a recombination that happens to have gotten mixed into a segment that looks like a match with someone else.
The two major companies have taken this into consideration and you won't receive matches that have a smaller than 5 cM segment. FamilyTreeDNA shows matches at 5 cM. For some people who prefer the 7 cM limit, this means that they might ignore some of their ftDNA matches. 23andMe shows them at 7 cM. However you can choose to share data with people who do not share enough DNA to be on your match list, but with whom you might share smaller segments (more on this later). You can also see smaller matches if you upload your data to Gedmatch.com, which allows you to choose your own settings. They recommend a minimum of 7 cM.
But those little segments aren't actually worthless. Each segment of DNA you have in common is yet another piece of evidence of the relationship. Say you have a match with one segment of 5 cM. Is that the only DNA you have in common? Or do you also have a smattering of 3 cM segments? It does offer up a tiny bit more proof of a relationship.
As a visual example, look at a match from my Great-Aunt Ree's list at ftDNA. She shares a total of 73.75 cM with a confirmed third cousin. Their longest segment is 23.89 cM, more than enough to be a "real" match. But she has a number of other segments that are much smaller (3cM or less). These segments add credence to the match, but on their own wouldn't be enough to confirm a relationship.
5 cM Additional cM
So matches with a minimum of 5-7 cM are reliable matches. How much DNA do you need to share with a match to have a chance at finding a common ancestor? For me, I have a confirmed common ancestor with someone who shares 26.76 cM, with the longest segment being 8.75 cM. We are 6th cousins.
I mentioned before that you can share data with 23andMe users who do not appear on your match list. Say you search for surnames on the site. You see a person who has one of your surnames in their profile. If they aren't already in your match list, it's because you don't share at least 7 cM of DNA (or you are capped out at 1,000 matches) You can send them a request to share DNA. If you view this person's DNA in "Relative Finder: Advanced," you might find that you share a small 4 cM segment or less.
A segment of this size is not enough to prove a relationship - but might hint at one. This is where testing multiple relatives comes in common. Say I share only a 3 cM segment. My mom might share 5 cM. My Great-Aunt might share 10 cM. If I had not test my mom or my Great-Aunt, I wouldn't be able to see the larger segments and would not have good evidence of the relationship.
So take-away here: trust the segments of 5 cM (or 7!) or larger and test multiple relatives. Hopefully this information was helpful and good luck cousin hunting!