For me, the most exciting thing is Digital Distribution. 

I was an early adopter of PS3 and 360 this gen, and both consoles had very low disk space when I bought them.

The convinience of having games on my HDD will be huge. HDD's will be much bigger so I'll be able to fit a ton of games on them, Games will be released on PSN/XBL on Day 1, and downloading (atleast on PS4) will be way better since you can now play while you download. 

Probably new IPs like Knack, and new ways to play like the GamePad.

Easily the massive upgrade in specs. With some much more power you we will see bigger game worlds with less limitations like more and better AI, physics will be better and ofcourse not to fussed but graphics will be better

Better uses for the Euphoria engine.... SOME ONE USE THE DAMN THING!

Things like Miiverse.

Didn't think I would love it as much as I do! being able to post screenshots etc and discuss with other fans is great.

Basically the whole package.. from the technical side - better graphics, Ai, animation and physics. To better stories, inventive/innovative gameplay, fresh ideas and new experiences.

Also getting rid of the terrible image quality of current gen consoles graphics. No more; sub HD resolutions, low quality AA/AF (or no AA at all), short draw distances, muddy textures, LQ shadows etc.

more games in the franchises I love

Super Smash Bros 4! Only game where Sony+M$ fans come to play on a Nintendo console without any wars :0

change: less emphasis on casuals and more for gamers!

I can't wait to see Halo 5 after the amazing graphics, sound, and gameplay of Halo 4. So I went with Better graphics/Special Effects. Advances in AI will be good too.