Excellent 3rd party developer in my opinion.
Up to the PS2/GBA era I was a PC-only gamer and never played a Japanese game except for FFVII on PC out of curiousity for a few hours (the controls were terrible). When I bought a GC and an Xbox, I discovered Nintendo, Sega (Skies of Arcadia Legends) and Namco (Tales of Symphonia), but not Square-Enix because I never bought a PS2.
It wasn't until the DS/Wii era that I really came in contact with Square-Enix games, which means their new games and many re-releases could not disappoint me but either not interest me or surprise me. The latter happened.
DS and PSP gave me tons of good to great S-E remakes/ports and new games:
- Dragon Quest IV, V, VI remakes
- Dragon Quest IX
- Dragon Quest Heroes: Rocket Slime
- Final Fantasy III, IV remakes
- Final Fantasy XII: Revenant Wings
- Final Fantasy: The 4 Heroes of Light
- Final Fantasy Tactics: The War of the Lions port
- Final Fantasy Tactics A2: Grimoire of the Rift
- Tactics Ogre: Let Us Cling Together port
- Star Ocean: 1st Departure/2nd Evolution ports
- Chrono Trigger port
- The World Ends with You
- Valkyrie Profile: Lenneth port
- Lufia: Curse of the Sinistrals
plus, on console: Final Fantasy XIII, Just Cause 2 (both bought for PS3), Star Ocean: The Last Hope (X360).
Still wanted, but unfortunately never localized:
- Sigma Harmonics (a unique and presumably very good DS game)
- Blood of Bahamut (DS)
Never played but I heard good things about it:
- Nier
Upcoming S-E games I'll definitely buy:
- Deus Ex: Human Revolution (Wii U version)
- Bravely Default: Flying Fairy
- Dragon Quest VII remake
Also, not to forget:
They got one of the two world's best videogame music departments, at least in my opinion. Quality-wise it's only rivaled by Nintendo, but unlike Nintendo S-E actually markets their music with an own label and a store.