Big name greats that many know:
Super Mario Galaxy 1+2
Super Smash Bros Brawl
Xenoblade
Super Paper Mario
New Super Mario Bros Wii (if you prefer more retro gameplay)
Zelda: Twilight Princess
Zelda: Skyward Sword (I personally prefer it over Twilight Princess, but to each their own)
Metroid Prime Trilogy (kinda hard to find, but currently not too bad in American Gamestops)
if the above can't be found, then get the first two for Gamecube and MP 3 for Wii.
Mario Kart Wii (BS rubber banding, but other than that, it has great controls and courses)
Kirby Epic Yarn
Kirby Return to Dreamland (kinda expensive to find)
Donkey Kong County Returns (though I prefer the 3DS port: lesser graphics, but with more levels and a better control scheme)
Fire Emblem: Radiant Dawn (also expensive to find)
Punch-Out
Wario Land: Shake It (again, for retro)
Wario Ware: Smooth Moves
The Last Story
Lesser Known Gems:
Prince of Persia: Forgotten Sands (IMO, far superior to the HD one, better gameplay mechanics, and lots of extras, love it)
A Boy and His Blob (Wayforward is a good studio)
Arc Rise Fantasia (HORRID English dub, but otherwise a very good JRPG)
Battalion Wars 2
Boom Blox and its sequel (fun block-breaking puzzles)
de Blob and its sequel (great platformers)
Dead Space Extraction (surprisingly good story and character models, only problem is lack of enemy variety)
Endless Ocean and its sequel (a slow, calming, underseas exploration series with great music)
Epic Mickey and its sequel
Excitebots Trick Racing (controls take some getting used to, but a good racer)
Geometry Wars Galaxies
Goldeneye 007 (a good remake, either for this or the later HD ports)
Harvest Moon: Animal Parade
Klonoa (excellent remake, vibrant and fun)
Madworld
Muramasa: The Demon Blade (has a slightly superior Vita port with more levels and a better translation)
No More Heroes and its sequel (I know you have them, I'm just making a list)
Pandora's Tower
Red Steel 2
Resident Evil: Umbrella Chronicles and Darkside Chronicles
Shiren the Wanderer
Sin and Punishment: Star Successor
SSX Blur (very involved and interesting control scheme that takes getting used to, but no voice acting, sadly)
Tatsunoko vs Capcom
Zack and Wiki
Godzilla Unleahed (like the DBZ game, lots to do and enjoy for Godzilla fans, like me, but is hard to find now)
Rune Factory Frontier
Rune Factory: Tides of Destiny (may have the subtitle "Oceans". Depends on your country)
Trauma Team
Silent Hill: Shattered Memories
Rhythm Heaven Fever
The Conduit (sequel isn't as good, imo)
House of the Dead Overkill
Fragile Dreams
Sonic Colors
Sonic and the Black Knight (divisive, like many 3D Sonic games, but I liked this one)
Little King Story
Phantom Brave: We Meet Again
Centipede Infestation (again, kinda old school, but its by Wayforward, and I think they are excellent)
Fortune Street
Port and Compilations that I think are good:
Rayman Origins (I prefer the Wiimote and Nunchuck control scheme)
Resident Evil 4 (I like this version's control scheme)
Dragonball Z Budokai Tenkaichi 3 (essential for any DBZ fan, lots to do and a fun control scheme)
Kirby's Dream Collection
Metal Slug Anthology (seven games in one)
Dragon's Lair Trilogy (for animation fans, like me)
Bit Trip Complete
King of Fighters Collection: Orochi Saga
Samurai Shodown Anthology
Okami
House of the Dead 2&3 Return
SNK Arcade Classics Vol. 1 (there was never more volumes)
And lastly, just a few that are just kinda 'okay', but interesting:
The Kore Gang (started as an Xbox game, and looks like one, but it has good art design, and if you like 6th gen 3D platformers, its right up your ally)
Musroom Men: The Spore Wars (similar story, except better graphics. Excellent art design, but very much like a 6th gen platformer)
Elebits
Dragon Quest Swords (not a fan of the in-town controls, but its combat is fun, and has good voice acting)
Tales of Symphonia: Dawn of the New World (a divisive JRPG, don't know if you'll like it)
And lastly, even though I know this site is very much against it, Metroid: Other M. No, I don't like the story or voice acting, but the gameplay I found to be kinda addicting, if a tad glitched.