In Golden Axe you can choose to play as one of three characters, with each having their own characteristics. Gillius Thunderhead has great attack power but little magic, Axe Battler the Barbarian has average attack and magic skill, and Tyrus Flare has great magical power but weaker weapon attacks. Each character has standard attack moves where successive hits on an opponent generate a "combo" of several different attacks. Your characters also have a rear attack, a charging attack, a throw attack, and a jumping attack. Each character has a magic meter of various length which can be powered up by collecting "Magic Pots" dropped by elves that you smack with your sword at various points in the game. At various points in the game you encounter enemies riding on "Bizarrians" such as Dragons. You can knock the enemy from the beast and ride it yourself, which gives you access to the beast's attacks until you are yourself knocked from its back by an enemy.
Overall, Golden Axe is fun in a 'classic' old-school sort of way. The setting, enemy and character design, music, pace, and gameplay are all very good and help to elevate it above its 'standard' gameplay and a banal fantasy plot. If you have played other versions of the game, you might be a little disappointed, though. Two thumbs up!