Are non-exothermic explosions possible?
Ultimately, explosions are just a type of spontaneous reaction, and even endothermic reactions can be spontaneous, so long as entropy increases enough over the course of the reaction to compensate it. Near room temperature, however, the entropic factor is usually small compared to the enthalpic factor. This is why there are comparatively few examples of reactions which produce strong cooling upon mixing reagents. 

That said, none of this strictly precludes slightly-exothermic or endothermic explosions, to the point that the concept has been legitimately investigated. As I mentioned in the comments, there is even a specific term for these types of explosions; entropic explosions.

For a spontaneous reaction to be explosive, there is one property it must have above all others: the reaction must happen very quickly. Now we are dealing with kinetics, which is much harder to analyse theoretically. It is possible, however, to point out another factor that makes endothermic explosions difficult.

By far, most reactions speed up when temperature is increased. In a conventional, exothermic explosive, this establishes a positive feedback effect, where heat from the reaction causes it to react faster, which produces more heat, which causes even faster reaction, and so on, facilitating a runaway reaction and subsequent detonation. If the exotherm is weak, then there is a larger chance that the explosion will fizzle out before enough heat is produce to get things going, or the reaction might be too slow to explode and instead steadily combusts. For an endothermic explosive, very much the opposite happens, and a negative feedback is established; once started, the reaction would decrease the temperature of the explosive, hindering propagation.

So, while there are no arguments which completely forbid slightly-exothermic or endothermic explosions, it seems to be a rather unlikely scenario in practice. Wikipedia only lists one possible contender for an entropic explosion, which is triacetone triperoxide. The original article making the claim is mostly theoretical, and there seem to be some rebuttals to it, so even that is not certain. Of course, we may be in the middle of a giant selection bias effect, because almost all research into explosives is focused on getting more energetic materials, not less. Maybe there are examples waiting to be found, but no one has had the interest in doing so!

As a sidenote, explosions actually don't necessarily produce gas. There are some rare examples, such as cuprous acetylide ($\ce{Cu2C2}$) and silver acetylide ($\ce{Ag2C2}$) where all the products are solids. Also, there are examples of non-chemical explosions which are only slightly exothermic or even endothermic. As MaxW mentions, a pressure explosion from a liquefied gas will be endothermic, as energy is consumed to evaporate the liquid. Another interesting example of an explosion which is probably only slightly exothermic is a Prince Rupert's drop being set off.