Altitude Limitations for Hot Air Balloons

What is the maximum altitude a hot air balloon can reach?

65,000 ft is the high altitude record for a hot air balloon set in 1988 by Per Lindstrand flying his Stratoquest balloon over Laredo, Texas.

Why is there a maximum altitude for hot air balloons?

Hot air balloons have a limit on the altitude they can reach. As they rise in the atmosphere, the surrounding air gets thinner and less dense so the higher the balloon goes, the less buoyant they are. Eventually, they will reach a point where they cannot displace enough air to off set their weight and they will begin to sink.

Gravity pulls air to the ground causing a build up of air pressure close to the earth, allowing balloons to be more buoyant.
http://travel.howstuffworks.com/hot-air-balloon5.htm

What role does air density play and why does it decrease as the you go higher in the atmosphere?

Density of air decreases as the balloon goes upwards. This is because the atmosphere is mainly concentrated in a belt of 6 km in thickness, held there by the force of gravity.  Gravity tries to pull all the air down to the ground but as more of the air is pulled down, the pressure and density at ground level builds up and creates an opposing upwards force. Thus in equilibrium in the atmosphere reaches a density profile which is approximately exponentially decreasing with height and the buoyancy force on a balloon decreases with height. For hot-air balloons, this sets a limit to how high a balloon can go. For gas filled balloons, such as those used to gather wind speed and direction data, the skin will rupture when it has expanded sufficiently at large heights. The pressure due to air at ground level is about 100,000 N/m2 (or ``Pa" after Pascal). (http://staff.science.nus.edu.sg/~parwani/htw/c2/node20.html)

Buoyancy is what makes a hot air balloon rise. It rises in air because the density of the hot air is less than the density of air. This produces a buoyant force :
Fb=(pair – phot air)Vg  which means you can have a mass of  m=(pair – phot air)V for a balloon of volume V. As the air pressure decreases in the atmosphere the air pressure in the balloon has to keep decreasing as well. Eventually there will be a point were the air pressure cannot decrease anymore in the hot air balloon.

I wonder which aircraft can go higher?  http://www.photohome.com/photos/hot-air-balloon-pictures/balloon-39.html

Resources

http://www.pha.jhu.edu/%7Ebroholm/l31/node11.html
http://www.challenger.virgin.net/Content/Crew_lindstrand.htm
http://www.ktca.org/newtons/newtonsclassics/classic2.html
http://staff.science.nus.edu.sg/~parwani/htw/c2/node20.html