Interesting thought. I started to come up with something, but it's really difficult to classify games into archetypes because games can be so different depending on different variables - era, designer, programmer, etc. If you're new, most people will lump games by designers and programmers. Very loosely and quickly I've broken them down into different archetypes in each category. It's a really rough list, and only covers some of the first things that came to mind.

Designers
Ritchie - known for fast and flowy games (Flash, HS, NF, ACDC, GOT)
Nordman - flow games, typically a 3rd flipper involved (i500, Wh20, DM)
Eddy - Flow, with a bash toy (in 2/3, anyway) (AFM, MM)
Borg - I think he's tough to pin down, he has a lot of variation in his games... (I know, that's really no help) (Tron, XM, MET, TWD)
Lawlor - "stop and go" is often used. Pick your shots, usually a 3rd flipper to a jackpot shot somewhere (TAF, TZ, WW, RCT)

Programmers
Johnson - very deep rules, think "epic journey" (pairs well with "stop and go" games) (TSPP, WOZ, LOTR)
Sheats - Simple to understand, but lots of strategy to maximize points, very clean and complete (usually pairs well with flow games) (AFM, SM, ACDC)
Sullivan - Simple rules, usually focused heavily on multipliers (SW Pro, GOT)

Eras
60s and earlier - keep the ball alive, score points
Early SS - A little more depth to rules, clear drop targets, rip spinners, etc.
Mid 80s (sys 11 era) - stories added to rules, help pinbot find his eyes, run away from the cops in HS, etc (PinBot, HS, WW)
DMD era - games become more complex and focus more on story (modes). Obtaining high scores often involves stacking, etc
LCD era - here we are... games have become even more complex - there are multiple ways to attack a game, with lots of minutia to obtaining maximum points