Just to humor the original poster, my favorite game of all time is "Rez", but I think that "Ikaruga" might be the most perfect marriage of intuitive, ingenious gameplay and effective conceptual design that I've ever experienced. Just effortlessly deep in a way that's so subtle, yet hits you like a ton of bricks when you finally pick up on the Taoist symbolism. "Rez", while its concept and design may not be as intuitively intertwined as "Ikaruga" just has that awesome "Panzer Dragoon" gameplay while combining it with ideas that I've always found fascinating, like synaesthesia, evolution, civilization, the universe as vibration, et cetera. "NiGHTS into Dreams..." was a long-time nostalgic favorite that hit new heights for me when I really started approaching it like an arcade game, then later on had a dream about the titular character and realized that the character therefore technically existed on its own terms. Started to make me realize why Yuji Naka gets so emotional about the game. "Shenmue" and "Seaman", in radically different ways, radically changed the way that I looked at what a video game could be.
If I were to pick a top 5, it would be:
Rez
Ikaruga
NiGHTS into Dreams...
Shenmue
Seaman
But since we're on a Sega site, those might seem a bit too obvious, so a top 5 for non-Sega games:
LSD: The Dream Emulator (PlayStation)
Download 2 (PC Engine)
Moon Remix RPG Adventure (PlayStation) (This game is in Japanese; a great English alternative would be Undertale)
Opoona (Wii)
Otocky (Famicom)
Basically, I like games that take advantage of the medium by putting me in a very different place, but don't lose sight of the fact that they're a video game, either.
In terms of game feel alone, apart from overall experience, Super Shinobi II, Sonic Jam/CD, and Batsugun get the highest marks from me as well.