I would point out that in many of these threads I think people are failing to make a distinction between a character and a series. Sonic for example isn't really a "series" anymore, but rather a character who gets plugged into very differant kinds of games. Simply put I have no real problem with the character per-se, it's just that the games they keep putting him in are garbage.
In general when it comes to cartoony games and such I really see no real reason why they can't use Sonic, but I think they need to be a bit more selective about what games get made as well.
For a long time I've sort of felt Sonic in paticular has suffered due to furries. I have nothing against furries per se, but a lot of them are huge Sonic fans, and buy a lot of his games. The idea behind things like "Sonic Vs. The Black Knight" and such titles seems to be vicarious wish fulfillment fantasies about like sword and sorcery furries or whatever. Also the ever increasing roster of anthromorphs also seems to be connected to this, pure gamers find it annoying, fur-fans, well they all the their favorites and which characters are appearing (even if briefly) can be a big deal in certain circles. I guess what I'm saying is that I think the problem is that Sega has gotten too fixated on non-sexual fan service with the character, rather than producing quality games. Such is simply my thoughts.
I think SIMILAR arguements can be made about other "series". Mario for example is a character that is goofy enough where he can be plugged into any game that doesn't take itself seriously. If your going goofy, might as well use him. However with Mario I think the focus has remained on the games a lot more than Sonic which is why he's found more annoying.
Final Fantasy is in a similar boat, given that it's pretty much a set of conventions that get attached to RPGs. I mean in RPGs a fire spell is a fire spell, I find no real problem to them using Fire/Fira/Firaga to designate levels and such, and in the end that's what it comes down to (conventions). The nature of Final Fantasy is simply that when I see something like a spell name, it might be in a totally differant world, but I pretty much know how powerful it is and what it does. I tend to see "Final Fantasy" as a set of general concepts than as a real "series".
Really, the only reason why I usually feel the need for an actual series to be "killed" is because it's one that I don't care for, and would have preferred the studio use the time and budget for something else.
I guess if I had to pick something that I think should go, it would probably be Grand Theft Auto. Not because it's BAD per se, but because I feel the developers can no longer do it justice. After the fiasco with "Hot Coffee" and cow-towing to censors with "Manhunt 2" I think Rockstar kind of lost it, and seems like they are pulling their punches. Heck, after those titles pretty much everything is going to leave that doubt in your mind.
I kind of feel the series "peaked" with San Andreas, and while GTA IV got praise for story and some spot on gameplay mechanics (not to mention a very complete package with all the TV shows and such), a lot of it felt like they were pulling their punches. San Andreas is kind of the last time I felt sure that they were making the game THEY wanted to make, as opposed to working around censors and moralists.
Games like Resident Evil and Silent Hill are still decent, but I think they really need to experiment a bit more. Resident Evil deserves Kudos for evolving with 4, but then it kind of stopped with 5. Silent Hill has tried to evolve, but really seems to be wallowing in a rut.
As some have pointed out (here on The Escapist for that matter) the most successful horror series evolved over time. Characters like Freedy Kruegar and Jason Vorhees became the icons they are because they were able to do differant things with them (some cool, some like 'Jason in Space' far less so... but they did try). Resident Evil mixed it up a bit in RE 4, decided the characters were no longer victims, so established protaganists became heroes instead of victims, and new monsters were unleashed. RE 5 pretty much downgraded RE 4 in most areas and didn't really seem to grow or evolve the way it could. Silent Hill ceased to evolve (IMO) because of fear of censors as early as Silent Hill 2, when they cut the game heavily because of complaints over the demo. Since the cutting of SH 2, every Silent Hill game has pretty much recycled pretty much the same material, and monsters. The last truely creative thing they did was "Pyramid Head" and truthfully the game seems to have sort of turned into an seriel horror fest that is all about having him pop up. The problems I had with some of the more recent games wasn't that the combat was too smooth or whatever (heck, not everyone is helpless), but the fact that it got predictable. Straightjackets that barf acid, killer nurses, and pyramid head. There was nothing that stuck out as NEW. Surrealism is fine, but when it's the same as every other game in the series... well that's a rut. The exception to me being SH 4, but then again that was not developed originally as a Silent Hill game. People complained about that game because it was differant, but I also noticed that the game hasn't exactly picked up a head of steam through the retreads that were Origins and Homecoming.