In no particular order--
Umihara Kawase (any version) - I have tinkered with it for a few moments on the SFC version, but it's not got a proper playthrough yet. It was enough to get me interested - they need to make more weird games like that! I recently lost an auction for the PSone version, and the curret one is kinda pricey.
Thunder Force IV, Elemental Master - Sega Genesis shooters, I actually bought both back in the day. I gave them about 15 minutes of playtime though, for some reason they never captivated me in the way their predecessors have, but they are still very much worth looking into (especially the former). To this day Thunder Force II and III (II especially) remain some of my favorite moments in gaming.
Hyperduel - same dev as above, and I've played through the MAME bversion of the lackluster PCB. The Sega Saturn version is supposed to be a worthwhile enhancement however, if I ever see it floating around for reasonable $$ then I will snap this up.
Gunstar Super Heroes - I loved the old Genesis title, and played this one for a moment.. it didn't grab me. But it's legacy (and the weirdness I have heard about it) definitely intrigues me. Treasure's an honest dev!
Killer 7 - Suda 51 is growing on me. As always I like weird, stylized games, so long as they have substance to them. This one sounds uberweird, but it's got enough of an underground following that it could be worth dropping a couple quid for. I'm interested to see where his new title "no More Heroes" for Wii goes, though I am not impressed with the tech of the screens I have seen. If I get a Wii I will certainly check these titles out. This guy reminds me of Clover Studios, for obvious reasons.
Space Raiders, Megaman Network Transmission - I recently scored both of these Gamecube titles for peanuts on eBay. Something I never do (buy game for a system I don't own?) but the system is cheap enough I could get it for peanuts as well. I may eventually, but more likely I may just buy a wii someday. Space Raiders is an odd-sounding descendant of Space Invaders.. it got skeptical press, but always sounded worth checking out to me. For some reason SI is still --hard-- to play!!! In fact the 1991 update is still quite fun, and yes even the original can be addictive as well. As for Megaman, it's a throwback to the sidescroller days using the "ick" new incarnation.. but I remember playing a build at E3 some years ago and being interested. Hey we don't see many side scroller platformers at all these days, and with a pedigree like this, it's bound to be worth a look (especially as the reviews were't awful)
Guardian Heroes, Burning Rangers - I am on some kinda vintage Sega Saturn kick lately. both of these were standout titles back in the day, I don't know how well they've aged but they are still referred back to even now. If i can find them cheap I'll jump on them. I have the GBA rom of the former but never felt tempted to boot it up, it didn't review too well anyway.
Wario Ware Twisted - the 2nd one in the series. I was a big fan of the first Wario Ware, and this one is often referred to as the "peak." Stupidly, I borrowed the game from a friend for >6 months but never looked at it once before returning it. I should just pick it up though. It's lik only 10-15 bucks!! If I do ever get a wii I'll likely get their Smooth Moves game as well, it's supposed to be alright. I am sure it's not great, but I get the feeling I would dig it.
Donkey Kong: King of Swing - this game always sounded appealing to me. old school gameplay (you just use the shoulder buttons and that's it). It's got a little bit of a following, supposedly it's a descendant of the old-old-HOLYCRAPold NES title Clu Clu Land. I should just flash it sometime. There's a DS followup in production as well, I wonder if it released yet though?
Drill Dozer - similar to above, a Game Freak-produced title (yeah, they make Pokemon besides.. and nothing else apparently!) for GBA. Noted as "the last cool GBA sidescroller," it was originally released in Japan as "Screw Breaker" which sounds cooler (and well yeah, sexier). It just sounds like it's easy and fun and good technique.
That's it off the top of my head. I could go on with my 2nd tiers but i'll let it chill out for now. Suffce it to say I have a ton of oldschool PCE CD-ROm games I'd love to check out, plus about 20 games on Nintendo DS which would probably suck me away for a good several weekends (if I ever caved in and bought a DS). Fodder for future writing, at least.
Time to get back to making games for the rest of you, then...