Now that every System is capable of HD visuals, do graphics really matter to you personally much? Before graphics mattered a ton to a lot of people but in this upcoming gen will it really matter? A lot of gamers decided to go with PS3 or XBox 360 simply due to Wii not having HD graphics. Now that Wii U does, can anyone really have an issue with them? 

I was playing Pikmin today and for some reason thought "this game looks really good" Since Pikmin is a GC game that released in 2001 and I thought they were good, I'm pretty certain I will be fine with whatever the next-gen has. So for me personally, I won't even care about the graphics when deciding which System to get next-gen. Obviously games were always the biggest factor but graphics did play some roll. Now I doubt they will play a roll for me at all.

Will graphics be important when deciding on your system of choice? Will they be important to most "core" gamers?

They do to me. I tried to go back and play some older games (San Andreas, Hitman Blood Money etc) and I find them to get boring very quickly. Also there are some features that I wish these older games had that their sequels have. For example in Hitman Blood Money you can't crouch behind covers like you can in Absolution and it's really annoying.

Only N64/PSX 3D graphics make me cringe for obvious reasons.

They do to be honest. They show that hardware progression is being made as well as power to make worlds larger and more diverse.

Not so much anymore, now that everything is so pretty already.

Depends. I can't stand to play some PSX/N64 games (Who thought realistic coloring was a good idea in low-res 3D games), but most games from PS2+ are acceptable. SNES games aged particulary well though.

I never gave a shit about graphics really.

Very much so, great graphics is all part of the experience.

its not just about graphics, a systems power allows it to do much more things in terms of AI, animations, levels, physics and alot of other stuff. but yes i do care about graphics, the better they are the more immersed i am in the universe of the game

3D gets old pretty quickly, and once you are used to seeing modern 3D it is difficult to go back. The crude polygons in PS1/N64 games make the games near unplayable now. The FF4 "remake" on DS made me cry on the inside.

2D, however, ages exceptionally well and even 8-bit era games are still highly enjoyable. The games of this generation that will age best are probably those that are 2D or pseudo-2D as well.