I should just copy and paste the last half hour conversation on AIM with my brother but no one reads logs so let's do this for reals.
The rule is, you can't just spit out an old series of games that you'd like to see a new title in. You have to say what they'd do to bring it up to the modern age. I'm fairly sure that's why a lot of them haven't seen new titles since the SNES days (or what have you.) Return-to-form is also acceptable for series that have churned out a lot of turds recently.
#1: Actraiser. Imagine a game where you fly around as a little cherub angel in a flying combat style engine, all while you're directing the townspeople to build their city. Break it up with an old-school side-scroller action (preferrably hi-res 2-d sprites, but I'd settle for what they did with Castlevania Chronicles for the PSP) every now and again when it fits in the story. If not that, then make 3d action platformer stages with combat similar-ish to the God of War or DMC games, except the twist is you're an angel (obviously for those that have played #1 and 2 back in the day). I'd probably prefer the later, now that I think about it, because its awesomeness potential is off the charts. I can imagine diving off buildings at super speeds to drive a sword through some imp's heart or something equally epic.
#2: Demon's Quest. I know that no one actually played Demon's Crest back on the SNES which is probably why it died as a series, but goddamn it I want to play as Firebrand again. Demon's Crest is one of the best games no one ever played. I don't know how they'd revive it but keep it fresh enough that people would want to play it, though. I think they'd have to go more like the original game back on the NES and Gameboy, where you explore somewhat RPG style and then "battles" are just short platformer style stages. (Kind of like Legend of Zelda 2, actually.) Again, I'd prefer to keep it 2-d when it comes to the Platforming. I don't think 3d would really work for Firebrand as it would the Angel dude from Actraiser. It probably wouldn't be for a next-gen platform, but for the DS or PSP. I can imagine it working pretty well on the DS. I'm sure Capcom could think of some fun touch-screen minigames or something that wouldn't draw you out of the world too much.
#3: The Lost Vikings. I know it's never going to happen now that Blizzard has it's cash cow and never needs to think of an original concept again, but damn it I love puzzle games, and puzzle games that pretend to be action titles? I approve. The 3rd dimension would require quite a bit of new thinking in terms of making the puzzles, but has awesomeness potential. Maybe add a new viking in there, too, although I have no idea what sort of deal he'd be.
#4: Secret of Mana. I know it's technically not a dead series, but the ones that people remember, the ones that actually have a contiguous playstyle that generated fans? We haven't seen one since Legend of Mana for the PS1. Square seems content on flushing it down the toilet as far as quality goes, but it really shouldn't be THAT hard. Hell, they could simply port or re-release Seiken Densetsu 3 in English this time so we can finally play it legally outside of Japan and know what the hell is going on. A return to form is all I'm calling for.
#5: Starfox. See Secret of Mana. A friend of mine pitched an idea awhile ago on the /v/ boards at 4chan that was actually a pretty good idea. They'd actually go BACK in time to Fox's dad. You'd play as the original Star Fox crew before they all started to try and kill each other. Keep it a railshooter. Toss in a landmaster level or two. Problem solved; series back to form. Back to being FUN. Considering how you can actually aim yourself now with the Wiimote, a railshooter would be pretty awesome.