Long-time reader, first-time poster. I think the issue with DNFs/Droppers/Whatever-you-call-them is actually two-fold. Or rather, any sort of solution to them is, and even then it still won't be perfect.
The first aspect is any sort of ranking/tracking method for showing on your screen how many games the player has completed. It's possible this may not be done at all; we've heard speculation all over the place about how Brawl's online play may just consist of the ability to play, being very bare-bones. If it isn't, then a match-tracking system likely could be done and should be done. Tracking "Matches completed" either as a number or percentage should be pretty easy. Anyone Dropping/DNF'ing would receive either a match loss, or have a decrease in their Matches Completed percentage, or both. Seems easy enough, and we already know some console games do this -- don't some versions of Madden have exactly this kind of setup?
There is the downside that anyone who Drops for a genuinely legitimate reason, such as a sudden unexpected power-surge turning their Wii off, will get a DNF on their match tracking. This is unavoidable, since the world isn't perfect (if it was, we'd already have Brawl). Fortunately, any honest player will have a low DNF percentage on their match-tracking unless they have some truly bizarre circumstances affecting them. So if they do have some sort of match-tracking, a DNF percentage indicator or similar seems fine. Those who do drop rampantly will be properly reflected.
But. But: Not all DNFers will care. Others may be more subtle about it, maybe even using multiple accounts if the game permits it. This is where the social side comes in, and the SmashBoards are a perfect outlet for this. Once Brawl comes out, you could have a 'Good Game' thread and a 'Bad Game' thread. Good Game would be for posting the names of anyone who plays a good, straight-up, honest match with you and plays it to the end. Note that since this is a matter of social honesty rather than Brawl skill, a player would not need to be Isai/Ken/etc. to be listed in the Good Game thread. So long as they play honest, their amount of skill should be generally immaterial. Just post their name and congratulate them on a fun session of Brawl, and move on.
For those that do drop under obvious circumstances (They're losing by a significant margin, etc.), posting their name in the Bad Game thread would be appropriate. Some level of restraint would need to be exercised here; if the player was still reasonably in the match and capable of winning when they DNF'ed, it could very likely be an ISP burp, power outage, or other legitimate reason to suddenly vanish from the game. Those instances would probably need to be given benefit of the doubt, presumption of innocence, etc. - Bad Game thread would be for blatantly obvious drops/DNFs. Skill should also be irrelevant here in the overwhelming majority of cases.
There are two benefits to this. The Good Game thread promotes community and sportsmanship, while the Bad Game thread will help you learn about DNF'ers before wasting significant time with them. The Good Game thread also helps act as a sort of defense against false Bad Game reports, in some cases.
There is the downside that people could engage in clique behavior, getting their friends to help them excessively or outright falsely mass-report a Bad Game person. The only solution I have for that is individual discipline: The person should be expected to keep civil and polite, and honest in their dealings. I've seen this work in other competitive-gaming communities.
Obviously not everyone will behave in the ideal fashion, and that's the inherent drawback to the social aspect of this. I don't know if there is a fix for that, or really even a fix for any system people might impose to help fight the DNF menace.
In fact, I'll come out and say it: There probably isn't a perfect fix. The best anyone could really hope for is a Good Enough solution to the matter, something that alleviates the problem even if it doesn't totally fix it.
Anyway, those are my thoughts on the matter.