Assuming protagonist role, male, and not yet mentioned as requirements, here are a few more red/gingerheads
• Western-developed game (and, incidentally, western-devised character)
• Character is "taken seriously"
Lester Knight Chaykin from Another World / Out of This World and Heart of the Alien:
Maybe also Spirou from the Spirou et Fantasio franchise (there's a handful of
16 bit-era games dedicated to the character):
• Western-developed game (and, incidentally, western-devised character)
George Jetson from The Jetsons franchise (many games):
Obelix from the Asterix franchise (many games):
• Character is "taken seriously"
Arthur from the Ghosts 'n Goblins series. His overall presentation is a little comedic, so, well, arguable, maybe?
It also has to be noted that his hair tends to be a little more reddish/auburn in some interpretations of him, and more brownish in others - not sure about the exact semantics or Capcom's canon here. Ultimate Ghosts 'n Goblins and original Makaimura artwork side-by-side:
Ark from Terranigma / Tenchi Sōzō:
Maxim from the Lufia series:
Todd Snap from Pokémon. Had his debut in the anime, and in Pokémon Snap on the N64, you assume his role from a first-person perspective. He's almost never seen in-game however, so maye he's too much in the background to be considered in this vein?
Last, but not least,
extremely serious Two Dudes from Two Crude Dudes / Crude Buster!
(Alternatively with morning star and cigar
)
• Non-human
Too many to count, probably ;o
Here are a few popular ones: Fox McCloud, Crash Bandicoot, Conker, Mr. Nutz, Bowser from 'Bowser's Inside Story', Blanka, Plok (is that a hairdo?), Nymn from Tanglewood, ...
kitten: Waffle Ryebread from Tail Concerto too - although it's one of these cases where there's a substantial difference between (cover) artwork and in-game graphics.