Fletcher is probably one of my favorite Redskins of this recent, dismal era, and he's now started 185 consecutive games. He's put together an incredibly impressive career for someone who was undrafted out of Division III John Carroll, but I'm not sure he's quite "Hall of Fame" caliber.
Honestly, for a long portion of his career, Fletcher was widely regarded as the NFL's best player to never make a Pro Bowl. He finally shed that label in 2009, and has made the Pro Bowl each of the last three seasons. But he's still just a three-time Pro Bowler, a one-time All-Pro (second team, 2011) and a one-time Super Bowl champion (of note, he's the last active player from the Rams Super Bowl winning team, which seems insane until you realize the Rams won that Super Bowl 13 years ago).
Fletcher has racked up impressive tackle totals year after year, but tackles are an unofficial stat and don't appear to have much correlation with which defensive players are in the Hall of Fame. He doesn't have a ton of sacks (34.0 in 226 games) or interceptions (19) or forced fumbles (18). He's basically been really, really good at stopping ball carriers for a really, really long time -- at least by NFL standards. To me, that leaves him in the non-existent Hall of Really, Really Good, not quite the Hall of Fame.
Of course, I don't get a vote on this, and it's entirely possible that five years after Fletcher eventually retires, people will look at his entire body of work, measure it up with the other defensive players up for vote and decide "you know what? London Fletcher IS a Hall of Famer." I certainly wouldn't complain.