A "classless" system, characters in GURPS are designed from the ground up using allotted points determined by the GM, with the option of acquiring more points by taking numerous disadvantages. Points are used to buy stats, skills, and advantages. Advantages are truly the meat and potatoes of GURPS, being the mechanic by which most characters are customized and differentiated from each other.
All task resolution in GURPS is done with a 3d6 roll which is compared to a target skill number. Lower rolls mean greater degrees of success, conversely, higher rolls indicate a greater degree of failure.
Problems
The biggest complaints tend to fall into 3 categories.
1. The inability of a 4-Stat system (Strength, Dexterity, Intelligence, and Health) to accurately depict a person's abilities.(Intelligence (IQ), for example is used to represent not only general intelligence but perception and willpower as well)
2. The godawful number of sourcebooks available and the inability for most worldbooks to stand alone without the aid of numerous other sourcebooks.
3. The ability to make truly silly characters, and similarly, as with any point based system, GURPS lends itself to Red-Mage-Point-optimizing twinkin' munchkinism of the worst sort. (One can make a highly intelligent character with the inability to learn, or whose sole skill is gravedigging)
Good things
GURPS, if nothing else, is EXTENSIVE. Even that word doesn't begin to encompass the sheer magnitude of things one can accomplish using GURPS. GURPS, is, incidentally, one of the few systems to address the concept of a society's technological advancement, measured in an arbitrary unit known as Tech Levels.
GURPS's greatest strength, however, is the ease with which it lends itself to customizability. Tinkering with the GURPS engine is not only encouraged, but elaborated and demonstrated in other sourcebooks. (Most of these rules are covered in Compendium 2). Don't like IQ representing Perception and Willpower? Make them seperate stats. There's even point guides on how to balance it out. There's guidelines and rules on developing new advantages and disadvantages, and style of gameplay.
While the ability to make that IQ:18 gravedigger is often cited as drawback of the system, I personally consider it a strength that such a silly character can be invented. I wouldn't allow it in my games, I'd force my players to make something more sensible. But the fact that the flexibility is there is comforting to me. It is that flexibility that the system strives for.
That flexibility is one of GURPS's major strengths, and it is the only system I can think of that is flexible enough to let you design completely original crossover genres. One can mix Ice Age with fantasy and scifi as easily as Feudal Japan with cybernetic vampires, or cyberpunk with a wild west flavor on Mars. Want to duplicate a favorite book or movie setting? Roleplaying system for said book/movie not out or planning to come out? GURPS is your best bet to try and design a setting based on your favorite movie/book/life/whatever.
Chief among the many complaints is that the system is rules-heavy, but here again is the ability to simply do away with rules one doesn't enjoy. Entire fights can be reduced down to a simple opposed 3d6 roll vs. another 3d6 roll, or it can be so convoluted as to take hours to determine a single fight, because a Spin Kick to the Head succeeded the Feint roll by 6, so I have the +6 to hit, but the head's -5 to hit, and are we using opposed combat rolls or just generic defence, and are we still using Passive Defense, and what's the penalty to do it with a wounded leg that's only taken 2 hits of damage, and I'm under medium encumberance....
You get the idea
Again, it depends strongly on the GM, and the system suffers or thrives depending on the amount of attention devoted to figure out what works and what doesn't. Odds are, as first-time players and GMs to the system, you won't figure out what works, it takes several sessions before a modicum of comfortability is established between players and GM's.
The only major weakness in GURPS that can't really be defended is the absurd number of sourcebooks available. While it is technically possible to run a session on just the main book alone, it's not terribly feasible. On the other hand, Steve Jackson Games's GURPS line is well known for doing their homework when it comes to writing supplements, so quality isn't generally an issue, just cost. At $20-$25 a book, one must pick and choose carefully which supplements to buy, and know what kind of world one plans to create. The more diverse the world, the more one will need. To try and copy Shadowrun, for example, would require, at least, GURPS Magic, GURPS Cyberpunk, GURPS Fantasy Folk, and probably Compendium 1. A generic fantasy game, though, will probably just need GURPS Magic and a working knowledge of medieval history, which GURPS generously provides in GURPS Low Tech, for $20. GURPS is highly enjoyable, but it must be admitted, it does appeal to a certain detail-oriented, left-brain mentality. Gamers used to a more dramatic, less detail oriented type of play, such as White Wolf's engine, won't find GURPS overly enjoyable. This is best exemplified by the nickname of GURPS gamers, "Gearheads," probably derivative of the (in?)famous GURPS supplement, GURPS Vehicles, that treasure tome of formulas for everything from hydrostatic lift to aerodynamic drag.
One of the more curious aspects of GURPS is that, after a while, you find yourself learning a lot about many myriad useless details. GURPS Low Tech, for example, provides such nuggets as:The first steam engine was invented in 1 A.D. by Hero of Alexandria; The Aztecs were so mathematically advanced as to have developed the notation for 0; and dried wood burns something in the neighborhood of 7,000 kilowatt seconds of energy.
Their worldbooks are equally detailed. And in the back of every book is a list of references and source material. Let it never be said that the fine people at Steve Jackson Games never do their homework.
Hydrogen has an approximate lifting power of 14.7 cubic feet per pound.
GURPS mechanics can be toned down to be enjoyed by those who prefer less detail-oriented gaming, but then, what would be the point?

