Should Sony/MS/Nintendo make games for Nintendo/Sony/MS?

No. As long as they make hardware they should not. The best way to differentiate the platforms is in this fashion. Take this away and the only person who gets screwed is the consumer.

@ OP: Others have said different between 1/2nd parties.

No. In fact, all third parties should go first party.

No. In case you have not noticed most of the best games this gen are first party games. or 3rd party exclusives.

Insomniac were 2nd party. They have never been 1st party. As for bungie i think they were first party bt MS sold them. I aint to sure though

I'll be first in line to get Capcom's console. <3

Only if by "first" you mean "second"!

Are you saying that Nintendo should make games for the PS3??

Insomniac and Bungie were second party.

First party, by definition, cannot go third party.

Bungie was first party, but then left M$, then joined Activision a little later

You have to love how everyone bitches about semantics knowing full well they get what the OP is saying instead of actually staying on topic.

And so I'm not a complete hypocrite-- yes, games going on multiple platforms is great for the consumers though I do believe exclusives have their place for various reasons.

Rare tried to go 3rd party back in 1998. Nintendo freaked out, bought into the company, let them start self-publishing games and built them a new state-of-the-art HQ. Then 4 years later Nintendo sold them off to one of their their competitors.

Nintendo also divested their interests in Silicon Knights and Leftfield Productions last gen, who then went on to make games for rival formats. They've been pretty reluctant to invest directly in western studios since then, though they've been throwing cash around like crazy in Japan the past several years starting up and buying out studios, beefing up their own internal studios and working directly with select 3rd party partners.