I have a very serious question for everybody - when was the last time you heard of anyone using a repeating crossbow?

I've never seen anyone - not an NPC, not a Player - ever use one because they're pretty much just not worth it. It does not stand up to scrutiny, however, when we consider how powerful the crossbow was in warfare during the time that it was introduced. In China, the Chu-Ko-Nu repeating crossbow could typically fire 40 bolts in a minute. In D&D time, that's a gut wrenching 4 bolts every round - something dedicated rangers can accomplish around the same time that wizards start being able to cast Circle of Death.

The most badass handheld crossbow wielded by europeans was called an "Arbalest". These massive crossbows were made of steel and could be shot once about every thirty seconds. The catch here, of course, is that it took about a month to train a arbalestier effectively. According to Wikipedia, Arbalests could be accurate out to 900 meters (2952 feet, or more than half a mile) and delivered 5000 pounds of force. They were so powerful that the Magna Carta attempted to ban all foreign crossbows from England, and were largely considered inhumane and unfair much in the same way modern warfare considers biochemical warfare, because a man with a month's training could take out a Knight in full plate and a lifetime of training.

Fancy talk aside, the problems remain

1. Bow Damage Potential is Massive vs Crossbow - The amount of force produced by a crossbow was much larger than a longbow. Having said this, however, we can look at the stats and notice that a longbow deals on average a single point less than a heavy crossbow, assuming that the longbow wielder has a 10 or 11 strength. This seems low.
2. Repeating Crossbows are Worthless - A Repeating Light Crossbow can be reloaded five times as a free action, before it must be reloaded as a full round action. A Longbow, which deals the same damage, can be reloaded as a free action an infinite amount of times and doesn't cost an exotic weapon feat.
3. The Only People Who Use Crossbows Are Weak - The only reason to use crossbows in D&D is either you aren't proficient with bows, or your strength would otherwise prevent you from dealing damage with a bow. The reality is, however, that a crossbow fires bolts as if an ogre was firing it from a longbow - with a TON of force.

1. Increase Heavy Crossbow Damage - A simple increase of the heavy crossbow to 2d6 damage would bring a niche role to the crossbow. A casual user could fire it once every other round, and a dedicated one could still only fire it once per round with Rapid Reload. With this, the Heavy Crossbow becomes more than just a Simple Weapon. It may be prudent to make the Heavy Crossbow a martial weapon and leave the Light Crossbow as is to provide for game balance in this situation.
2. Make "Repeating" a Quality - Adding the "Repeating" quality to a crossbow costs 200 gold and makes a crossbow one catagory harder to use. Combined with the previous suggestion, Repeating Light Crossbows would be martial weapons on par with bows, and a Repeating Heavy Crossbow would be an exotic weapon worth taking.