What could cause halogen bulbs to explode?
"One exploded after an hour" as indicated by @fixer1234 this is caused by finger oils or other contaminates on the lamp envelope itself (not the reflector).  Its very important not to touch anything but the outer edge of the reflector.  

Further what type of fixture is this bulb being used in?  If the fixture is open faced situation such as this:

then the MR16CG must be used, (the CG stands for "Cover Glass") which has a self-contained lens.   I mention this specifically because CG versions of the bulb tend to be harder to find and many people don't know when to use the CG version VS when the open face bulb is ok (i.e. enclosed fixtures). 

"We regularly have bulbs dying" is likely a socket problem, replace the bi-pin socket the lamp plugs into. When heat is generated by the lamp pins this type of bulb will prematurely fail. (I know as hot as the lamp gets while burning this is hard to reason, but when the bi-pins generate heat from poor connection the result is premature failure.)

In the end, the best advice is to give is find an LED replacement that you are happy with.  Unfortunately in many situations the MR16 halogen type of bulb is the hardest to replace with LED. It's very difficult to find LEDs that burn as brightly and with the colour clarity of the original - highly energy inefficient heat generating - halogen.