I know Alundra, great game and original concept too (I mean, this psychological thing of getting into people's dreams, etc.), it reminded me of Zelda Link to the Past, though... but with more complex graphics (another good point of the game). It would have been one of my fav, but in the last part the game is very difficult.
LOD is another great game too, but has the same problem: the last part is still too difficult if compared with the rest. You should try Legend of Legaia, though the graphics is not as good as the "rivals" of the same genre, the story is beautiful and the OST is just sweet.
I don't know the other game, but maybe someday I'll try it.
Future Cop LAPD is a new discovery, I started playing by coincidence before it was posted here, I only had a demo of it but I was impressed by the gameplay, really funny, still have to finish it.
I remember the EA intro was funny for me and friends because it sounded like... "Electronicartsartsartsarts..." ;D
Resident evil 3
Final fantasy 7
Tekken 3
Strider 2
Castlevania sotn
RE3... well, a classic!
FF7... I don't know, I always felt like Square's game hate me. Vagrant Story, for example... one of the best game I've ever seen, but how I wished it was more of an arcade game then something so technically complex.
Tekken3... another great classic.
Strider 2... gotta try it.
Castlevania... I don't know, I was terrified about the difficulty and strange gameplay of the NES version. The required timing of gameplay gives me nightmares, but the screens look fine.