RPG's similar to The Adventure of Link?...

[ZOM]

Arise!

If you have a PS3, 3D Dot Game Heroes might interest you.
Video here: http://www.youtube.com/watch?v=9UvYWMSRAVo

Personally, I can't wait till this game get's released; It looks soooo fantastic!

[BryanM]

Video here: http://www.youtube.com/watch?v=9UvYWMSRAVo

Heh, looks pretty cool.

But! It reminds me I need some way to not read Youtube comments.

Someone's already mentioned EVO The Search for Eden right?

[Shelcoof]

Wonder Boy in Monster World (Genesis)

You Beat me to it!!!

I also suggest

Wonder Boy Monster Land (SMS, Arcade, PS2)
Wonder Boy III Dragon's Trap (Dragon's Curse for PCE) SMS, PS2
Wonder Boy IV (translated version available) (Mega Drive, PS2)
Tomba! (PSX)

Wonder Boy Games can be purchased on Wii's VC or emulated.

I own both original copies of Wonder Boy III Dragon's Trap for the SMS and Wonder Boy In Monster World and the Sega Ages Compilation for the PS2.

Games are excellent in every way imaginable for such an old game.
I promise this is probably one of the best side scrolling action adventure RPG you'll play.

Tomba! is another amazingly fun game for the PSX, you just have to play it and enjoy.

Edit: Videos added

Wonder Boy III Dragon's Trap (Dragon's Curse)
http://www.youtube.com/watch?v=Pl7T6kBDQA4

Wonder Boy Monster World
http://www.youtube.com/watch?v=MZ38Ss73Tsk

Monster World IV
http://www.youtube.com/watch?v=bPs2UYlo0J4

Wonder Boy Monster Land (Master System version)
http://www.youtube.com/watch?v=MMb9_Uhe9uY

Tomba!
http://www.youtube.com/watch?v=5s3dYiU4v0M

ENJOY!!!

[scrilla4rella]

Tomba! is such a classic. Probably THE best side-scrolling RPG/Adv game I've ever played. The Wonder Boy games are def worth checking out.

[Regulus]

Zeliard has been mentioned a few times, and I recommend it as well. Great DOS side-scrolling adventure game with excellent music.