1. System can fade to the background to run games (i.e., not too much chart referencing, looking up rules, etc. needed), but with a decent amount of crunch rather than narrative (i.e., not interested in some collaborative style where PCs spend a point to do some large change to a scene).
2. Some sort of "curve" in dice roll results (whether a fuller 3d6 bell curve, a 2d10 not a curve but close enough, etc.), rather than a flat d20 sort of resolution (I find that flatter dice systems tend to use Hero/Fate/Action type points for re-rolls, etc. to help control the wide randomness of systems like d20, I'd rather the dice handle that themselves and minimize such points).
3. System doesn't hide the math or make understanding likelihood of success hard (i.e., d20 is very clear on chances of success, but L5R hides the success and needs a chart to understand what one's chances are to succeed).
4. Point-buy rather than class/level-based (okay if costs increase as scales higher, like Star Wars D6 skills, etc.).
5. Damage save rather than hit point type systems (though some mix of may be okay).
6. Works for regular level as well as superhero.
7. Can accumulate equipment but not be unbalancing.
8. Uses stat+skill (plus roll) for determining outcome success (stat can vary based on applicable circumstances).
9. Uses regular dice and not cards, weird dice, etc.
10. Those above are just off the top of my head, may add more.
11. Armor soaks damage rather than makes harder to hit.
12. Not a lot of character backgrounds/careers/lifepaths, really looking more point-buy oriented, in part because too much of those end up making it hard to make PCs in one's head away from the books
13. Not dead stats (e.g., odd stats are largely dead in DnD, a lot of stats in Hero are dead (e.g., for Int, just get 13, 18, 23, etc. due to skill roll rounding, etc.)
14. Minimize obvious min-maxing, feat taxes, etc. (e.g., in Mutants and Masterminds, have to max your 4 factors of attack, defense, damage, and toughness, vs Savage Worlds, where one might want to increase damage or toughness and no "right" or "mix-max" choices).
15. Easy to get characters built and/or players up to speed to play (e.g., like Star Wars D6 or Savage Worlds).