GURPS

Character creation in GURPS is detailed, but slow.  There are no levels or classes, just points, which can be used to buy attributes, advantages, disadvantages, or skills.  Different campaigns start with different amounts of points, so that (for instance) a superhero can start out as a more powerful character.

Attributes

GURPS has four attributes: Strength, Dexterity, Intelligence and Health.  Strenght and Healthy just define the character physically, while Intelligence and Dexterity are combined with skills to make skill checks.

Skills

Skills are how characters accomplish things in GURPS; for instance to shoot someone you would use the "Guns" skill.  Skills are based on attributes, so for instance you might buy the Guns skill at a "Dex + 1" level.  If you later improved your Dexterity, you'd similar improve your ability to shoot ... or do anything else physical.

Advantages

Advantages cover any non-skill benefit a character might have, such as a high pain threshold, wizard training, or the ability to move objects with their mind.  Advantages can also be further be customized with enhancements or limitations, allowing you to gain more or less powerful versions, that cost more or less points as a result.  This can allow for a nearly any power you can imagine to be described as a GURPS advantage.

Disadvantages

Similarly players can also take disadvantages for their character, such as Code of Honor or Blind, to gain extra points.  All together this system allows for incredibly individualized character, including almost any you'd want to re-create from fiction or real-life (in fact, there are multiple GURPS books with stats for historical NPCs such as Ghengis Khan) ... but it can be a bit overwhelming to newcomers.

To succeed at an action in GURPS, players roll 3d6 and attempt to rull under a target number, which varies depending on the action.  Most of the time the actio will be a "skill check", meaning the player will have to rul equal to or less than the character's relevant skill. 

Critical Successes and Failures

If you fail a roll by more than 10 you critically fail the roll, and the GM decides what terrible fate results.  Similarly if you beat the roll by more than 10 you instead get a critical success, dealing extra damage or otherwise succeeding with flair.

A Note About 3d6 (vs. d20 or Other Dice)

3d6 results in a far more predictable distribution of rolls than a single die roll (typical in other systems).  Think about when you roll stats for a Dungeons and Dragons character: you usually get a lot of more 10's and 11s than 3's and 18's.  In contrast, every d20 roll has an equal (5%) chance of rolling a 1 or 20 as it does a 10 or 11.

This allows GURPS to have critical successes and failures, but have them be rarer and more dramatic, while leaving most rolls with fairly predictable/average outcomes.

Hexagonal Grid

GURPS uses a hexagonal grid for combat.  Hexes offers a benefit vs. square grids, when it comes to diagonal movemen: in square grid games (eg. D&D) characters moving diagonally move more quickly ... but since hexes don't have corners, they don't have this problem.

Initiative

Unlike most games, GURPS does not have a random element to initiative.  Instead, characters always move in order based on their basic speed (a stat derived from their Dexterity and Health scores).

If one group surprises the other they can potentially get several seconds of actions before their opponent can react ... and since a single round of combat in GURPS lasts a second, that can be significant.

Maneuvers

On their (one second) turn a a character can take a single maneuver, plus any number of free actions (eg. talk or drop an item).  A maneuver could be to move, attack, or move and attack (at a penalty), as well as other options such as aiming or feinting.  A character who moves can move a number of yards equal to their basic move (ie. basic speed with fractions rounded off).

Attacks

To attack a character makes a skill check with the appropriate weapon skill, applying a variety of modifiers for things like the target's size, range, and speed, or the weapon's accuracy bonus (if they took the time to aim), the lighting conditions, any cover the target has, etc.

Active Defenses

If the check succeeds the target can then opt to make an "active defense". There are three options: Dodge, Block (eg. with a shield) and Parry (with a weapon), and ranged attacks can only be dodged.  Active defenses are also a skill check, for Block and Parry; to Dodge you simply roll your Basic Move + 3.

If the active defense roll succeeds, the attack misses.

Injury

If an attack roll succeeds the attacker gets to make a damage roll, which will vary based on the weapon they use and other factors (eg. ranged weapons do half their damage when far enough away from a target).  If the defender is wearing any armor they can subtract it's "DR" (damage resistance) from the damage, and the rest goes through.

Depending on the type of damage dealt, it might be multiplied now (eg. cutting weapons deal 1.5x ).