Savage Worlds

As with most games, Savage Worlds characters have attributes, in this case five of them (essentially the D&D attributes, without Charisma).  Attributes are measured as a die type, so a weak character would have a d4 Strength, while an incredibly strong one would have a d12.

Players can also select a race for their character (or remain human to get an extra edge), and a number of skills.  Just as with attributes, skills have die-type-based ranks.  Raising skills higher than their associated attribute costs double, but otherwise there are no restrictions, so you can make a cowboy/hacker/biologist if you so desire: there are no class limitations.

Finally a player selects Edges, which provide special benefits to the character, similar to feats in Dungeons and Dragons or advantages in GURPS .  To gain edges characters can take on hindrances (similar to GURPS disadvantages).  Every edge costs the same in Savage Worlds (no varying point costs like in GURPS), and there are only two levels of hindrances (Major and Minor; one major or two minor provides an Edge).

There are also a somewhat limited number of hindrances and edges compared to some other generic systems, but this isn't necessarily a bad thing.  While it does mean less customization options, it also means new players can review their options much quicker, speeding up character creation overall.

To succeed at an action in Savage Worlds, you roll a die based on the associated skill, and then also roll a separate "wild die" (a d6).  Either dice can "ace" ("explode"), which means that if you roll the maximum number on the die, you get to re-roll it, and add the result of all the rolls together.  You can then choose to keep either your original die or the "wild" one (whichever rolled higher), and if that die's result is 4 or greater (after any penalties), you succeed.

Players also start with "Bennies", and can earn more during play through good role-playing.  These "Bennies" can be used to re-roll any roll, giving characters another chance to succeed at critical actions.

When it comes to combat, Savage Worlds uses a deck of regular playing cards to determine who goes in what order.  The higher the player's card, the sooner they go in initiative, and if a player gets a joker as their card they can go at any point (and also get a bonus to their rolls that turn).

Between it's wild dice, "aceing" (ie. exploding) dice, bennies, and jokers, and various other factors, there are a lot of ways to succeed even when your skills are low, although of course higher skills are clearly a benefit.  All of this leads to a system that's more "fun" and cinematic, but also a bit less realistic, and also potentially more "swingy" (compared to, for instance, a system like GURPS).