Of course, the actual randomness of the number is up for debate, as many computers generate the numbers based on internal clocks. Some use the background noise of the universe to generate a set of random numbers at the beginning of each day (such as http://random.org), and in either case whether the number is truly mathematically 'random' is determined by your particular philosophy on the nature of existence, whether it is all predetermined or truly random.

True enough that at the very lowest level, random number generators based on CPU clocks are essentially pre-determined. However, when it comes to simulating a dice roll, randomness shouldn't necessarily be defined purely as 'undetermined', but as equal likelihood of all values (i.e. an even distribution). Even the background noise of the universe could for some reason have an unnoticed pattern (you'll have to look at the distribution of the numbers generated). 'Purely non-deterministic' doesn't necessarily mean you'll get an even distribution either--values can be tailored to various constraints (e.g. electron orbitals, which are essentially probability density functions in space), which is why for the sake of dice-rolling, I think CPU-generated rand functions are 'random' enough.

Back in the good ol' days, you just bought a book.

Ah, the good ol' random number tables

I'm with nehash on this one.

The practical question should not be "Are computer generated rolls 'truly' random." The question should be, "Are they as or more random than using your hand to toss a piece of molded plastic onto a table top." Rolling by hand isn't "undetermined" either. In fact, there are probably fewer variables involved in the results of hand-tossed dice than there are in a randomizer function that uses background noise from the universe. :-)

QFT. I knew a player that could roll a d20 and get whatever result you told him too each roll about 90% of the time. He could also talk backwards, only one word at a time though. I tried recording it once, it was surprisingly coherent when played back.

Absolutely, but both cases are moot if you believe that all events in history are predetermined by a higher being (Determinism) or if all things are randomly occurring according to no higher plan (free-will). Of course, it's a sliding scale so a person might believe that major events, such as the creation of the universe, were determined while other more minor events, such as your die roll, aren't.

World of L_Tiene has covered most of this in her answer, but I thought it might be worth adding in my perspective.

GURPS isn't the only roleplaying system that requires you to roll under a certain number, it's just one of the more well known ones. Warhammer and it's sub-systems also do that, and I'm playing in a game system called Flashing Blades that does the same, although Flashing Blades is a little known RPG.

From my own perspective of learning GURPS in the last 3-4 weeks, I didn't find it difficult to pick up. Part of the ease of the GURPS system is that by comparison in R≥S systems, the GM sets a TN, applies modifiers and then you roll (or mods are applied to the roll, it makes little difference), all of which requires having some sort of comparable scale between different sorts of tasks (easy, medium, difficult, etc.) This can cause some disputes and requires a delay while you ask questions.

With R≤S systems, you already have the TN given to you: it's the stat/skill you've got on your character sheet, so you already have a fair idea of your odds of success without having to ask any questions from the GM. In my GURPS game, I know I can make a roll and have some idea whether or not I might have succeeded before mods are applied.

R≤S also allow skills to rise as high as you have points to spend in them. In Warhammer they use a d% and you can get to 100% and even beyond. That is, there really is no cap on how high I can take a skill/stat except in some cases for it being prohibitively more expensive. With R≥S systems there is (ultimately) a desire to have the skill stat as low as possible relative to the TN to make it easier achieve the desired outcome.

Is this true, since when R=S it means success in either syatem?

I honestly only skimmed the thread, and I'm no where near smart enough to comprehend most of it (a man has to know his limitations) . If you're asking yourself why GURPS does what you deem counter-intuitive, you have remember the time it was created. In 1985 (I think that's when GURPS) came out, D&D was owned by TSR and they were having a tough time of it largely due to negative publicity, but also because there were other games out there now. Champions (which when on to become Hero System), Traveller and Twilight 2000. All three of those systems had you roll under the target number. So what seems counter-intuitive to you now, was pretty much how it was done back when the game was created. Also if you look in the credits of GURPS editions 1-3 you'll see Champions (or Hero System) listed as an inspiration.