Looking for some good turn-based strategy games.

I'm a big fan of turn based strategy games such as Fire Emblem, Advance Wars, Jeanne D'Arc, etc. and am looking for some new ones. I doesn't matter really which platform it's on, though I would prefer either psp, or ipod touch as I think this genre works great on handhelds. Other platforms I have available are PS3, 360, and PC. Now for some reason I wasn't able to get into the Disgaea games, and Final Fantasy tactics was just a little too much for me, but I'll happily take any suggestions.  Thanks guys!

the only hanheld turnbased "strategy" game i played was pokemon 
 
if you want a real turn based strategy game id check out civ 5

Final Fantasy Tactics Advance on the GBA is pretty good. It's a lot easier than the original FFT, and it's very addictive. 
 
There's also Final Fantasy Tactics Advance 2, but I haven't played it.

Most of the games you are listing aren't Turn Based Strategy (tbs) but Turn Based Tactics games. Turn Based Strategy games would be like the Civilization series or Europa Universalis. X-com is probably one of the most famous examples of such a game on the pc (the Might and Magic series also is pretty noteworthy), but the games you list are more in keeping with the japanese Tactical RPG genre, in which case I'd recommend something like Valkyria Chronicles, which has a mesh of tactics turn based gameplay and real time gameplay.
 
Primarily, I play these sorts of games on pc (I play pretty much everything on pc :/), and so I can't help but turn you in the direction of the King's Bounty series, as it is one of the most recent and best Tactical Turn Based RPGs.

Total war and Civ is what comes to mind. Though those really don't have what comes in the way of RPG elements like you are used to playing. You can find those on steam.

Fire Emblem everything. That is all.

the campaign mode in Medieval II has taken over my life.

Highborn on the iPhone is pretty alright, and it's got a great sense of humor. Cheap, too.
 
And Tactics Ogre: Let Us Cling Together is new on the PSP. That one's a classic, and this version is supposed to be fantastic. It's VERY similar to Final Fantasy Tactics, though, so you may not be into it.
 
I could make a few DS suggestions, but you say you don't have one, soooo... Those are the two that come to mind off the top of my head.

" I'm a big fan of turn based strategy games such as Fire Emblem, Advance Wars, Jeanne D'Arc, etc. and am looking for some new ones. I doesn't matter really which platform it's on, though I would prefer either psp, or ipod touch as I think this genre works great on handhelds. Other platforms I have available are PS3, 360, and PC. Now for some reason I wasn't able to get into the Disgaea games, and Final Fantasy tactics was just a little too much for me, but I'll happily take any suggestions.  Thanks guys! "

Just remembered a couple more. Shining Force is old, but a classic (I know it's on the iPhone and Xbox Live Arcade. Might be on PSN, too. Also available in Sonic's Genesis Collection, along with other games in the series), and I haven't played it myself, but Valkyria Chronicles may appeal to you.

I haven't played it yet, but Saiyuki: Journey West just came out on PSN for $5.99. I'm going to pick it up and try it out soon. I didn't like Final Fantasy Tactics Advance because it wasn't as deep as Final Fantasy Tactics, but it may be what you're looking for. I also haven't played Tactics Advance 2.

You can try out Battle for Wesnoth. It has 6 or so factions, multiple campaigns, multiplayer, and HEXES! I really like it, and you can get it on PC/Mac/Linux for free.

Just started Tactics Ogre: Let Us Cling Together, pretty sure the FFT(A) team worked on it.

" Just started Tactics Ogre: Let Us Cling Together, pretty sure the FFT(A) team worked on it. "