Out of the big 3rd party publishers, which one is your favorite? What's the definition of "big", you ask? Well, no idea, but I'd say these are the top 10 by size and variety of IPs, in no particular order (you may disagree):

EA, Activision Blizzard, Ubisoft, Take Two, Warner Brothers Interactive, Square Enix, Capcom, Konami, Sega, Namco Bandai.

Out of those, my favorite is Ubisoft. I own more games from them than any other one. I love AC (except for AC3 *shudders*), Rayman and recently South Park. Even my Japanese learning game on DS is made by Ubi. They seem to be bringing a few new IPs on next gen, delve into diverse genres (Child of Light is basically a "J"RPG) and support all platforms better than the average big publisher (Wii U, Vita).

If you want you can write your top 3/5/10 or whatever because why not.

I am going with Capcom ONLY because they used to make many awesome games back in the day like Breath of Fire III, Mega Man X, Mega Man 2, Viewtiful Joe and Street Fighter 2 ( among others).

I guess mine would have to be Take-Two, Konami, Namco Bandai, Sega and Square Enix

Take-Two cause GTA, nuff said

Square Enix cause even though they fuck up from time to time with things such as FFXIII and the Original launch of FFXIV, they do manage to release stuff like Bravely Default and Deus Ex: Human Revolution

Konami cause MGS and some Castlevania games

And Namco and Sega cause they release a shit ton of jrpgs and other games such as Tales and now Persona for Sega

Capcom, because most of their games appeal to me. I am clamping sega with the first party and taking into consideration mainly this last gen. Bioware and bethesda please me greatly aswell.

Capcom. They've done some odd things but they've still brought out some of the most enjoyable and diverse games to this day.

Funny, I think I could easily find some shit in pretty much every one of those publishers, be it anti-consumer policies, bad game related decisions, bad business decisions, straight up turds, heavy franchise milking etc.
My favourite from that list is probably Take Two.

Right now the third party companies sites I check roughly weekly are...

1. NISA
2. Atlus
3. XSeed / Marvelous
4. Tecmo Koei
5. Namco Bandai
6. Aksys
7. Idea Factory
8. Sega
9. Ubisoft
10. Warner Brothers

Square Enix. While they do keep managing to screw up from time to time they also own Eidos which have some nice franchises such as hitman and deus ex but square itself isn't all that bad seeing as how they do good in handheld space.

Hard question, don't really have a high opinion of 3rd parties right now. I am going to say Ubisoft because of Assassin's Creed

I want to say SE, but 13 was garbage to me. If what they said is true about them realizing their mistakes, and going to make jrpgs again are reality then I'd place them back on top, but until then they're just meh to me.

That being said I voted for Namdai...I love the Tales series and SC despite their niche appeal.