Sorry if I’m hi-jacking the thread, but have you heard of MAME for your computer? It will allow you to play just about all of the old school games on your computer:
The closest I’ve seen are strategy RPG’s. Battles are fought on levels laid out like a chessboard, and each turn you can move and attack with one of your fighters. The RPG element comes in between battles, where you can equip your characters and teach them new skills. There are tons of these types of games, but the ones I’m aware of:
Disgaea: clever, anime-style game where you play as the Prince of the Underworld trying to take back control of Hell. Lots of slapstick humor, coolest bit is that you level up weapons by going inside them and fighting battles. Very good.
Front Mission series: strategy RPG with battle mechs.
Saiyuki: fairly lackluster game, but some good characterization.
Final Fantasy Tactics: as we’ve learned, the best game ever made.
Some of the variants arrange the battles so that you take all of your turns, then the enemies take all of their turns. One of the coolest bits of FF Tactics is that the turns are staggered and based on a character’s speed. So your ninja will almost always have the first turn in a battle, for example, and some fast characters can get two turns in before a slow one gets his first turn. Casting spells or using combat abilities can increase a character’s speed, moving them up in the battle queue. You can end up doing really cool stuff with the turn order, like setting up a massive, area-effect spell for an area, luring a bad guy into the blast radius, and then getting your guy out just in the nick of time before the spell goes off.
The other coolest thing about Tactics is the job system, which gives it tons of variety and replayability (I’ve finished it about 5 times, using a different approach for the main character each time).
There may be “real” RPG’s that are turn-based on consoles, but I can’t think of any at the moment.
I just picked up a copy of agame called “Mojo!” which I can only describe as a well-rendered combination of Breakout and Marble Madness. I got it at KB Toys, in an aftermarket clamshell, with a xeroxed piece of cover art, but it was well worth the $4 I paid! Not sure if you could actually find this game anywhere or not. But if you come across it in a bargain bin, pick it up.
Yup, I’m quite familiar with emulators in general and MAME in specific, but since they’re techinally illegal, I don’t think the SDMB doesn’t want us talking about them. But thanks for the suggestion!! 
What I’m hoping for is new old-school games, if that makes sense.
Sol: those sound a whole lot closer to what I want. I don’t mind reflex “twitch” games, and I don’t mind role-playing games, but to me, never the twain should meet.
Necros: I’ll try to find it!
A local used game place will sell me a used PS2 for $150. I can get 'em on eBay for about $100 or so, but it’ll cost $20 shipping (give or take) and it’ll be a pain to return. Does $150 (plus tax) sound like a decent price or would it be better to just get a new one for $180+tax?
Fenris
Do you have a membership to a place like Costco or Sam’s Club? They often have a pack for 250-300 dollars that will include a mem card, another controller, and a game, at the very least. I’ve never bought one of those for any system, but it would be worth looking into if you’re comparing prices.
If you’re looking for modern versions of old school game styles, might I suggest Contra: Shattered Soldier.
If you’ve ever played a Contra game and enjoyed it then Shattered Soldier is for you.
For more old school-like goodness might I also suggest:
Shinobi
Maximo, and if you like it, Maximo vs Army of Zin
Gradius III and IV
MDK 2 Armageddon
Klonoa 2
If you’re looking for quirky Japanese fare, like others have said, the best stuff eventually comes over. Culdcept is a funky RPG that mixes Monopoly rules and with a Magic-like card game that is more fun than it looks like it should be. Then there’s Mr. Mosquito, a game that puts you behind the wingspan of a mosquito who goes around having to suck the blood of people in a house. It’s weird, and the controls take a little getting used to, but come on, it’s a game where you play as a mosquito!
And if you ever look into a GameCube, get Ikaruga, it’s a revelation in 2D topdown space shooters.