Let's start by disproving that 11-20 is the highest threat range possible in D&D 3.0/3.5.
Take the Improved Critical feat, which doubles your threat range. Also take Disciple of Dispater (Book of Vile Darkness, 3.0) up to 8th level, which triples it. These abilities explicitly stack. D&D multiplication rules turn this into a quadruple modifier.
Use a weapon (which must be iron or steel for DoD to work) with a natural 18-20 threat range. Quadrupled, that's 9-20 from one 3.0 book and the Player's Handbook.
Combining 3.0 sources: 7-20 or even 1-20?
Sticking with 3.0, we have the Weapon Master class (Sword and Fist). Its 7th level Ki Critical ability increases a weapon's threat range by +2. If this stacks multiplicatively with DoD (which it probably does), we have (3+2)*4 = full 1-20 crit range. If it stacks additively with DoD, we have a comparatively unimpressive 7-20.
Answering the question of whether it's possible to get both DoD and WM to the required levels pre-epic in 3.0 is left as an exercise to the reader.
There is also the 3.0 Stump Knife (also Sword and Fist), which has an interesting property:
Against foest to whom you have dealt damage during the course of a continuous melee, the stump knife's critical range is doubled (17-20).
So for the small price of losing a limb, we can increase the multiplier to x5.
3.5 and 3.0 together: Very hard to tell.
3.5 did lots to nix the range-stacking that was rather popular in 3.0. Muddying the waters are changed critical stacking rules, how those interact with DoD, and whether the Exotic Weapon Master from Complete Warrior counts as an update to the 3.0 Weapon Master.
One specifically 3.5 crit-enhancer is the 7th level of Streetfighter Barbarian, which grants a +1 to your threat range when charging.
Honorable mentions: Things that don't apply
Taking up to the 7th level of Psychic Weapon Master (3.5) is frequently mentioned. This doesn't actually work with DoD, as PWM works with crystal weapons and DoD with weapons of metal. (The Aptitude weapon enhancement from Tome of Battle also doesn't work, as that one applies to feats rather than class features.)
Serrated weapons are also frequently mentioned in discussions (increase threat range by +1). These are 3rd party additions, not from D&D books. Chainblades (a native 17-20 range) fall in the same boat.