Well, there's aren't that many dragons in the game, but the ones that are there are cool. They all start out as basic dragons, but you can change their class based on alignment.
I have one of each of the 3 types of Dragon:
The Black Dragon is the Evil type
Red Dragon is the Neutral Type
and Silver Dragon is the Goody-two-shoes-though-technically-dragons-have-4-feet-so-I-guess-that-makes-him-goody-four-shoes.
Mine are classed up to "Tiamat," "Red Dragon II," and "Gold Dragon," respectively.
There's one more class for each dragon to attain: "Zombie Dragon, "Salamander," and "Platinum Dragon."
You can get dragons really early in the game, just by roaming around the mountains on the first couple maps. They attack you as a random neutral character, and you can ask them to join you, and they always do (I've never been refused yet, but it may be affected by your charisma score).
You can also get dragons later, if you level up your Beastman all the way into a Dragon Master (which you can do by level 12) , then you can just hire all the dragons you want.
I suppose technically you could make an army of ALL dragon units! But there are lots of other troop types you will probably want to have:
https://www.gamefaqs.com/snes/588541-ogre-battle-the-march-of-the-black-queen/faqs/74349
I like the dragons to go along with my main character though, even if I can only keep 2 dragons in my unit at a time. So I keep the more evil-y dragons with me... and I let the good dragon go with a different goody-goody unit, because your reputation suffers if you liberate towns with evil units...
The game itself is like, uh, tactical combat? You put your units together and steer them around the battlefield (in real time, though you can pause and issue commands) and liberate towns, find hidden treasure, and fight the enemy units until you can defeat the main boss at the castle on each different map, while leveling up and equipping your troops.
If you like that kind of game, then definitely give it a try. It may take a little time to get into this type of game, and it's a bit slow-going at first until you learn the in's and out's, but the in-game-tutorial-ing is pretty good.
I'm playing the SNES version, but I think there was a PS1 version too.
Oh, look at that; I made an actual quality contribution post, and it won't even give me +1 to my post count! Oh, the unfairness of it all! I shall now whine about it for days upon days and lament the unjustness of the cruel, uncaring, empty world, while the peasants mock, deride and throw moldy fruits and brown M&M's at me! Woe, despair, and agony on me!! Deep dark depression, excessive mystery!!
*back to my game of Ogre Battle*