So, GameCenter CX and this thread have motivated me to finally start a Famicom collection. Game recommendations?
Akumajou Densetsu (Castlevania III with a built-in chip for extra, higher-quality sound channels that the NES wasn't able to use)
Devil World (a fun and comparatively varied Pac-Man clone from Miyamoto, Tezuka, and Koji Kondo of Mario/Zelda fame, and Tezuka and Kondo's first game)
Ninja Ryukenden III (Ninja Gaiden III, but unlike Western versions, this has unlimited continues)
Erika to Satoru no Yume Bouken (cutesy, Japanese text-heavy adventure game, but with
a killer soundtrack and
a legendary hidden rant by a staff member)
Ganbare Goemon 2 is already most of the way to what made its sequel Legend of the Mystical Ninja on the SNES great
Heisei Tensai Bakabon is an adaptation of a cartoon series based around a sort of Japanese Homer Simpson-type character, except this particular version of the series was set well in the past. Lots of unique platforming that changes based on the specific context of the stage at the time. Your character plays like he's overweight, and it works for the game. I want to say that it almost reminds me of a Wario game with the oddball sensibilities that entails, but it really doesn't play like one at all.
Takahashi Meijin no Bouken Jima 4 (Adventure Island 4), this one's a nonlinear Metroidvania sort of thing, unlike the others
Joy Mech Fight (Nintendo-made Street Fighter clone with Rayman-looking robots)
Labyrinth (not the *greatest* Gauntlet clone, but definitely quite playable, and every Famicom could use some more 8-bit Bowie and Jim Henson)
Ninja Jajamaru Ginga Daisakusen (a game by Jaleco with a slight control learning curve that's more or less every bit as competent a Mario 3 clone as Konami's Tiny Toon Adventures)
It's a little thick on Japanese, but Mega Man spinoff Wily & Light no Rockboard is a pretty fun game, kind of a more video game-y, faster-paced version of Monopoly. Making Dr. Wily pay you the equivalent of the hotel costs at Park Place/Boardwalk is incredibly satisfying.
If you're interested in seeing Mario 3 through a new, more difficult lens, when you get hit in the original Japanese version, no matter what suit you're wearing, you shrink all the way back down to little Mario, instead of going back to Super Mario as an extra intermediate step. Think of it as like a Mario 3 hard mode, if that's new to you?
If you liked RBI Baseball, Namco has tons of sequels that are more like the big-headed original than Tengen's RBI sequels as part of its Famista series, and as old sports games, I would assume that they go for fairly cheap.
There's all kinds of additional fun that you could get into with a Famicom Disk System as well, but I've heard that those are prone to hardware failure (the belts in the drives can be brittle or broken by now), and then you have either a second outlet or tons of C batteries to worry about. Still, stuff like Nazo no Murasamejou (linear, action-based Zelda with samurais and ninjas!), and Kid Icarus/Metroid/Zelda 1 and 2 with higher quality audio (and saving instead of passwords for the former two) are pretty cool, if you can live with the added load times.