Ok, so I've been trying to learn what I can about the starter. I feel like I understand the main point to be to multiply viable yeast. Some people are talking about the health of the yeast. One guy even mentioned how he didn't do a starter, but had more than enough yeast cell count, and yet still had no activity in the fermenter. But with that guy for instance, if he didn't have activity in the fermenter, would he really have had activity in the starter?
If a yeast becomes healthy and active in a starter, granted that I add enough yeast cells to my fermenter, shouldn't it have just the same effect in the main wort?
All right, let's tackle this one bit at a time.
Yeast health: So, the longer yeast is stored, the fewer "healthy" cells there are. Healthy cells are in stasis, but ready to be awakened by higher temperatures and abundant food (aka wort or starter solution). If you get fairly fresh yeast in a smack pack or dry yeast satchel, it should have enough cells to innoculate 5 gallons of 1.060 of ale (approximately); for the liquid vials I believe it's something like 1.040 instead. There is, however, a catch to the numbers; yeast that has been sitting too long probably has a lot of dead cells, so the time the yeast has been sitting is very important. All yeast products have either a manufactured date or a "best by" date, if you look at the online yeast calculators they all include this because the rate of yeast death when stored in proper conditions is fairly well known. In short, if your yeast is very old (and very old varies depending on the yeast type) then you might need to make a yeast starter even if your yeast should (theoretically) work for beer that you have. In short, try to get fresh yeast and be wary of yeast that has been sitting for two months or more, if it has been sitting that long a starter may be required.
Fermentation didn't start: So, there's a lot of posts like that on this site. 90% of the time the cause of fermentation not starting is either simply a bad yeast smack pack, vial or satchel or that the poster didn't properly pitch their yeast. Even if you vastly underpitch, you will see yeast activity, it's just that you'll get some very funky flavors, so in those instances you are correct that a yeast starter wouldn't help (though it is worth noting that a failed starter would show that the yeast was bad before it was pitched if that is the issue).
The bottom line for starters: If your beer's gravity will be slightly higher than specifications for your purchased yeast (usually 1.060 for an ale using a smack pack or dry yeast satchel) or your yeast is old, a starter is likely required. Otherwise, properly pitch your yeast (either by using a smack pack per instructions or rehydrating dry yeast) and ensure you have fermentable wort and everything should go just great.