In GURPS 4E if you're armed with a sword and a shield you can attack twice with the All-Out Attack maneuver or both block and parry the same attack with the All-Out Defense maneuver. However, if you're armed with two weapons the rules don't allow more attacks and you're less able to defend yourself!
Am I reading the rules wrong? Is it really pointless for an ambidextrous character to wield two weapons?
Please limit answers to the the basic rules.
What a second weapon can offer you, using only basic rules, is a second parry.
If you're highly skilled with a weapon type, let's say Rapier, then you will have a high Parry score with that weapon. Parrying twice with the same weapon is at -4(-2 for fencing weapons like the rapier) and therefore usually a terrible(fairly bad) idea, but with a second weapon you can parry a second time at no penalty*! This is useful against multiple enemies, in particular.
What All-Out Defense allows you to do, is to apply two defenses against the same attack.
In non-basic rules there are more things, like a Dual-Weapon Attack or Cross-Parrying.
It doesn't really benefit your offense, which is realistic, but it does help your defense.
*With Ambidexterity. Otherwise -2 for off-hand parrying.
Edit: After seeing your edit, I want to add that this will not cost you a lot more points. Ambidexterity is useful for all kinds of stuff, and this way you'll likely need to keep up one less skill...
With two weapons, you can attack with them both, by using All-Out Attack (Double), from p365 of Basic. The sole advantage over attacking twice with the same weapon is that you can do it with weapons that need to be readied after use. However, most characters who use such weapons only use one, plus a shield, and expect to use the shield as their main defence.
The real usefulness of two weapons comes if you buy Extra Attack, from p53. This is not cheap, at 25 points, and you'll want Ambidexterity as well, if you're limited to Basic, but it does give you potentially twice the damage output. It is available to normal people, but as always, consult your GM.
GURPS Martial Arts is full of advanced combat rules and options, plus real-world and fictional martial arts styles. For example, the Off-Hand Weapon Training perk allows you to buy off the -4 off-hand penalty for a single point, for a single type of weapon.
