There's a ton of stuff I look at and say “yeah, that should be part of the game.” Here's where I list out stuff that I should play/watch/listen to that directly relates to the game in some way.
Probably the most obvious influence would be MW2:21CC. I'm pretty much lifting the core mechanics directly from this game, and it's because they feel so damn good. The way the mechs handle really make the player feel like they're piloting this massive machine of force and destruction. On top of that, the look of this game, though technically dated, is a master class in effective use of low-poly models. The limitations of the time made for mechs and environments that were clear-cut, and they look sleek and sharp to this day.
Alpha Waves is a revolutionary PC game, largely considered to be the first true 3D platformer. It's simplistic graphics are again a major inspiration, as they are largely minimalistic but incredibly effective. Also note the use of bright, vibrant colors (though I'm fairly certain these were chosen more due to the lack of options on EGA graphics, rather than any color theory).
Another early 3D title, this time released only in Japan for the X68000. It's a first-person mech combat game with a focus on platforming and double-jumping, doing copious amounts of damage on the enemies you land on. It's also got a killer soundtrack and some great low-poly and pixel art.
The original Wipeout games (Wipeout, Wipeout 2097 and Wip3out) are all amazing titles, but I'm using Wip3out here because I own it. Of note are the in-game billboards and design (courtesy of the Designers Republic), the vehicle design (clean and crisp, good silhouettes, excellent color schemes) and environment design (futuristic but very believable). Also, the soundtrack is AMAZING.
FAKE EDIT: The menu and loading screens. I know it sounds crazy, but goddamn are they a beautiful example of clean and modern design.
She goes by plenty of other monikers, but Vektroid puts out some amazing experimental synthwave and vaporwave tunes. Her Macintosh Plus release is classic, and she's got new music coming out today (2/15)!
Only one EP out by this artist, but it's a good one. Very early '00-esque trance. I also really dig the design work done for the tracks, good typography there. Listen to it on Soundcloud.
Also known as Mirror Kisses and ESPRIT 空想, he does a great job of combining synthpop and vaporwave sensibilities (and without the overuse of sampling, which is super cool). Give 100% Electronica and virtua.zip a listen.
Awesome bit of acid house from the early 90's. Also, the album art is perfection. Listen to it on YouTube.
A cool looking but poorly written 80's sci-fi action film featuring a tank-like mech called Gunhed. Effects were created by the same team that worked on James Cameron's Aliens. For the most part Gunhed is a big inanimate mech on treads, but it looks cool. Also, the atmosphere in this movie is awesome; very dark, lots of fog, and nice laser effects.
I could take literally any frame from any episode of this show and make it into a color palette for the game. Also a good source of inspiration for architecture and level design; the 80's Miami locales are about as rad as it gets.
Classic 80's mecha cheese. An entertaining way to kill 90 minutes.
80's car design could be an excellent source of inspiration.
Some wonderful soul uploaded every issue of Spy Magazine, an influential satirical periodical that ran from 1986 to 1998, to Google Books. Everything from the type layout to the photography and advertising is a treasure trove of material ripe for replication and imitation.
A collection of imagery of various types of architecture and environments. Good inspiration for level design.