You left out the part about new versions of Linux coming out each month or so. One or two of those versions will be labeled the new "it" version and people will clamor to it until the next "it" version comes out. Mint Linux is a perfect example, it is the new "it" (ie hip, cool, etc) version and will remain so until it is replaced by the next latest greatest version of Linux. When that happens most people will dump Mint Linux for whatever is next leaving just a few stragglers behind. Then the cycle will repeat itself about a month later. And people wonder why Linux community can't get themselves all on the same page.
Lets look at the major (in market share) versions in North America of Linux that I recall.
First there was Slackware. A very early distribution and still around but aimed at the truly knowledgable.
Redhat the first commercial Linux to be really successful. Still around after years and still among the leaders of the pack. Its been in the black for years. Apparently they are going to begin marketing preinstalled Redhat to businesses on desktops. HP is marketing them on the Desktop in Australia now.
Suse. Now owned by Novell but originally a German distribution (and I believe derived from Slackware. Currently being pushed by ... Microsoft of all companies.
Ubuntu. The only recent one (Oct 2004). Unlike the others they are targetting the end users desktop and due to popular demand are being marketed that way by Dell.
Do minor new brands pop up and gain a following? Definitely, but unless they have something new they stay on the fringes. There are some that have tried for the Big Time but didn't make it Corel (now Xandros - Debian derived), Lindows (now Linspire and now Ubuntu derived), Simply Mepis (now Ubuntu derived).
There are also those that have big followings in other areas of the world, Mandriva for example (formerly Mandrake and Connectiva) is popular in Europe and South America in spite of almost being destroyed by "professional management" brought in by venture capitalists.
There are also those that have a large amount of influence but I wouldn't really say market share. The King of those is Debian. Its influence is shown by how many distributions are derived either from it or from a derivative of it (Debian to Ubuntu to Linspire/Mepis/Mint etc as an example)
Linux Mint does not make the list as it is NOT one of the major versions. I only found out about it from reading an English Linux magazine. I recommend it not for "cool or hip" but because from my viewpoint for many people it has reached the point of being "Good Enough". One way for me to tell that is because it finally allowed me to change from primarily Windows (2000Pro) but using Linux as well to the reverse. Outside of various things where
you may be experiencing a vendor lock in it is good enough for the average (non gaming) user. Gaming is the primary reason my other machine still has Windows on it.