I want to play the Ace Attorney games but I'm not sure in which order to play them, is there a right way?
 
Also, any plans for new games?

1) Phoenix Wright 
2) Phoenix Wright Justice for All 
3) Phoenix Wright Trials and Tribulations 
3) Apollo Justice (Personally, I skipped this one and moved to Miles Edgeworth, didn't lose anything) 
4) Miles Edgeworth 

I only played the first game before I played Miles Edgeworth, and it doesn't feel like I missed anything important. My guess is that it doesn't really matter in what order you play them. However, I don't see a reason not to play them in the order of release.
 

Disregard the opinions of anyone that says Apollo Justice can be missed.  A game that turns Phoenix Wright from a bumbling idiot into the ultimate chess master is awesome.  If there is one game worth missing out of all of them, it would be Justice For All.  The cases weren't that great, and Franziska was really the only good thing about it for me.

Just play them in release order if you can, though the only part thats really necessairy is playing the original first. playing apollo justice last would probably be good too.

" Just play them in release order if you can "

You have to play them in the correct order.  For a game that's basically story-driven, I have no idea why you would want to mix the order up.

" Disregard the opinions of anyone that says Apollo Justice can be missed.  A game that turns Phoenix Wright from a bumbling idiot into the ultimate chess master is awesome. "

I started playing this series last week myself, I'm on the very last case of the original game and I'm going to be playing them in release order, although I did contemplate playing miles Edgeworth 4th after hearing about the chronilogical order of the games. But I think I'd like to get the same experience as the true fans of the series.

Play them in order except play Miles Edgeworth before Apollo Justice.

Release order.

I played them in the following order:
Phoenix Wright
Apollo Justice
Justice For All
Trials and Tribulaions
Miles Edgeworth
 
It seems the original trilogy (PW, J4A, T&T) feed into each other quite a bit but in a very superflous way.
You could pick up any of the games without any prior knowledge and get along fine.
Apollo Justice is an unusual title in the series, the whole game being very cleverly linked within itself, and with some interesting uses of characters from the other games.
I would highly recommend AJ. Quite possibly my favourite of the lot...
Oh and it uses all of the epic DS specific controls of the final chapter of the first game which don return until AJ and ME. For that alone it's brilliant

In release order, presumably. That's the reason I've yet to crack open my copy of Justice for All.

Play them in order. 
 
Although I found the second one to be the most boring, except for the last turnabout. 
 
I wouldn't skip Apollo Justice, as some have suggested, it's a pretty great entry. Phoenix's character is awesome, and it uses the DS features in ways the 2nd and 3rd games do not.

" 1) Phoenix Wright 2) Phoenix Wright Justice for All 3) Phoenix Wright Trials and Tribulations 3) Apollo Justice (Personally, I skipped this one and moved to Miles Edgeworth, didn't lose anything) 4) Miles Edgeworth  "