What went wrong that made 

Saddam Hussein lose the 1991 war.

There are of course many factors, but military equipment is by far the least of it. There have been hundreds of examples of battles and even wars won throughout history by a side with seemingly inferior equipment. Lets start at the top:

1. Grand Strategy. You might wonder why George H.W Bush thought it was so important to build a huge coalition and assemble a massive army in the desert of Saudi Arabia, especially over what seemed to be a relatively simple dispute over the ownership of oil fields. The Grand Strategy of the United States is to increase its wealth and political power through trade, and an important sub set of that strategy is to ensure American allies and trading partners (not always the same thing) have access to cheap energy. Saddam’s seizure of Kuwait threatened the stability of the Middle East and free flow of oil to Europe, India, Japan and China, so had to be opposed. If Saddam wasn’t threatening the stability of the Middle East, then the United States would have never acted in the first place.

2. Maritime Power. The United States, after using its diplomatic muscle to assemble a coalition, used it’s incredible mastery fo maritime power to move tens of thousands of men and machines half way around the world, in ways that the Iraqis had no way of countering. The build up took over six months. Imagine sitting there for six months watching the largest force assembled since WWII arriving at your doorstep with no way to stop it.

3. Theatre and operational goals. The United States was leading a coalition with fairly clear and limited goals. President George H W Bush had no intention of removing the Ba’athist regime or committing to long term occupation (unlike the neo cons who shaped US policy post 9–11, but more similarly to the present Administration, which also does not wish to be ensared in nation building). Everyone in the coalition was working towards the same ends, and the goals aligned with all the partners (reestablishing the stable political order of the region). Operationally, this limited the movement of the forces to the borders of Kuwait (certain exceptions could be made, but this was never supposed to be more than supporting the main effort, not an effort of its own).

4. Tactical differences. As many people alluded to, the United States was trained and prepared to utilize “Third Generation” warfare, essentially manoeuvre warfare directed at displacing the enemy from their strengths through use of speed as a substitute for mass, and utilization of air, sea and even space power to enable this. The so called “Hail Mary” encirclement was anything but; it was a carefully calculated manoeuvre to get behind the main Iraqi defensive lines and collapse their position. The Iraqis were set to fight a second generation warfare battle, fixated on firepower and causing enough casualties to break the will of the Allied political leadership and ending the war on their terms.

The Iraqi dispositions also reflected a successful PSYOPS campaign, causing them to assemble large forces to repel an amphibious invasion which never came.

5. Superior training and organization. Also alluded to in other answers, the Allied forces were trained in manoeuvre warfare, and were quite capable of conducting large movements without needing to be micromanaged. Iraqi units down to the platoon level were essentially paralyzed by the need for their chain of command to closely supervise every move. The inherent flexibility allowed the Allies to act and react far faster than their opponents in almost every situation.

6. At long last we get to equipment. The Iraqi Army was one of the largest and most modern forces in the region at the time, with plenty of armoured vehicles, artillery and all the other tools needed to fight their planned “mother of all battles”. However, even when things were potentially favourable for them, they simply could not match allied training and equipment. The Battle of 73 Easting is perhaps the best example. (Paraphrasing from many different sources) The Allied advance caught the Republican Guard division by surprise, they were unaware that Allied GPS navigation allowed them to move through essentially trackless terrain. The Americans engaged rapidly on the move, but the Iraqis initially reacted as if they were under air attack, apparently not comprehending the speed at which the American vehicles were firing and moving at. The Americans were confused as to why the Iraqis didn't seem to be shooting back, until later when they “walked the battlefield” and found 125mm APDS-FS “Darts” from the 125mm cannons of the T-72’s stuck in the sand 1800m from the Iraqi positions. M1s were firing from 3000m, and the after action reports showed notches cut through the sand berms which surrounded the Republican Guard tanks by the 120mm American rounds, which then went on to penetrate the turret armour of the T-72 and cause catastrophic “cook offs” of the ammunition in the Iraqi tanks.

The sort of dug in positions the Iraqis were fighting from

While there were some obvious overmatch differences, the T-72M and M1 Abrams are from the same “generation”. If the Americans were fighting with M-60’s, upgraded with GPS navigation, digital radios and thermal sights, the primary difference would be the 105mm cannons would require the Americans to come within 2000m to strike effective blows, and it may have taken several hits to penetrate the berms and destroy the Iraqi tanks. Since the Iraqis would still be hampered by doctrine and command and control issues, the outcome would essentially have been the same.

Warfare is a complex, multi variant endeavour. The Americans excelled at almost every level, from the Grand Strategic down to the logistics (the true reason for the American and allied victory was the massive army of trucks that supplied all the aircraft, fighting machines and soldiers on the ground). The war was already lost when the Americans could assemble a coalition, while the Iraqis could not prevent that or assemble their own, and when the Allies could move into position entirely uninterrupted by the Iraqis. Had Saddam realized that and made overtures before Desert Shield was completed and Desert Storm launched, history might have been very different. Desert Sabre - the ground invasion of Kuwait, simply hammered the final nail in the coffin.