Rygar is probably best known for its NES incarnation, which was a non-linear adventure game (in the style of Metroid and the recent Castlevania games) that was actually pretty widely played by those who owned the system in the 1980s. Lesser known is the arcade game that started it all; which is a shame, because in some ways this is the superior game of the two.
This version of Rygar is entirely linear and has no overhead levels, but the graphics are much sharper and the gameplay is a bit smoother. Rygar handles a little better than he does on the NES, the collision detection is less iffy, and he has a more robust range of moves with which to protect himself against the constantly spawning onslaught of monsters. You can twirl your Diskarmer around by pressing Up+Attack, and throughout the game will pick up upgrades that extend it's reach and make it fire straight upwards to hit those pesky hovering enemies.
The game starts out surprisingly easy, but give it six or seven levels and the challenge level really ramps up. Actually, to be honest I've never even completed this game - even though you can continue infinitely from where you died, there are just so many levels I tend to get bored and quit (I know there's at least twenty). Don't take that as a negative recommendation, though - it is pretty fun for awhile, and I'm notoriously impatient with games so the average player will probably enjoy it for longer stretches than I do.
* Gameplay Video