Turn based Strategy games are some of the best especially when they have RPG elements. X-com Final Fantasy Tactics, Fire Emblem and the new Ghost Recon: Shadow wars are some good examples of good Turn based strategy games with RPG elements.
Disgaea tends to get bogged a bit down in the Grindehouse. It does have all the fun elements and can be very enjoyable but in the end it's not very stimulating because most your fights you win are because you are a high level, and not because you fought intelligently. But let's go down the whole list.
Dragon Quest is your standard turn based combat game, and it's basically what i think you want to avoid. Samey turn based combat where it's less about having good tactics and more about being a high level.
Final Fantasy stopped being turn based a while ago. Don't touch it unless you enjoy real time pre planned combat.
Doofus is sort of a turn based MMORPG and while it does seem like it could be fun I found it to be tedious, again another level and gear based one, where your tactics don't matter much.
Fire emblem is generaly good, but it's usually too easy to be a meaty challenge, and the sad part is it's probably one of the more difficult and unforgiving turn based strategy games out there. You get a small army worth of characters with different strengths and weaknesses. the more they fight, the more they level up, and the stronger they get, so if you don't use a certain charecter don't expect to ever be able to use them. The games are unforgiving in that if one of your units die, they are gone forever, but you can keep playing the game and just endure the loss of that unit. This makes the game deep and involving but mainly means you spend a lot of time reloading when your favorite character get's one shotted by someone who got a lucky crit, or you didn't notice had a special weapon made just for killing your favorite guy. It's fun and rewarding, but the latest one, shadow dragon is piss easy and hardly worth playing because of it. The one for the Wii, is balls acheing hard, So it might be difficult to find one that's fun for you right now.
X-com is a really solid one because it has a lot of different aspects that you have to keep your eyes on. Your tech level, and what kind of weapons you are capable of getting out into the field. Your solider levels don't matter so much, but better soldiers are better, so keeping them alive is good. And the overall state of the world. The game is a struggle to keep the aliens from taking over the world while you try to scrape together enough tech to mount an offense against them. This makes X-com deep and involving, while the tactical battles are fun, and have enough teeth to make you try to be careful and cover all your bases. It can be a little hard to get your hands on, if you don't like steam, but if your interested enough you can go ahead and check it out.
Xenogears, that came out for the play station store recently is another decent turn based game, it has it's own problems not related to the turn based combat, but it's a bit deeper than say Final Fantasy. Maybe check it out, if you don't mind it being for the PS1.
Final fantasy tactics is some good solid Turn based Strategy but it can be difficult to find, and all the entries on the DS are garbage. Find the PS1 version or give it up.
Ghost Recon, like I mentioned earlier is a new one for the 3DS, if you have one I would suggest picking it up. It's the most promiseing turn based strat game I've seen in quite some time.
If your looking for older games, Ultima and the old DnD games like Champions of Krynn and Curse of the Azure bonds are really good, they are just really old and confusing and could end up pissing you off pretty badly, if you can even get them to work.
And the last one I'm going to point out is Breath of Fire Dragon quarter. This is an innovative and creative look at turn based combat, but I point it out only as an example of how bad it is. This is certainly creative and strategic turn based combat, but the game just is bad... really bad. From start to finish. If you can find it, and are feeling brave, give it a shot, but don't hold me responsible for your loss of sanity.