The nature of momentum?

I'm not a physics major or anything so I don't know much beyond the basic newtonian stuff taught in introductory college physics. One thing that's always bothered me though is how during collisions, momentum is always conserved but not kinetic energy. Wikipedia gives me this: "It can be shown that a perfectly inelastic collision is one in which the maximum amount of kinetic energy is converted into other forms. For instance, if both objects stick together after the collision and move with a final common velocity, one can always find a reference frame in which the objects are brought to rest by the collision and 100% of the kinetic energy is converted" My question is: if you start out with said reference frame, then won't the final momentum of the system be 0 also since the objects are stationary? What's wrong with my logic?

To answer the last part first, if the reference frame and inelastic collision is such that the final momentum is zero then the initial momentum was zero the begin with.  Momentum is a vector quantity.  This means in particular that in one dimension you have to think of momentum has a signed quantity.  So the momentum of the object traveling to the right is subtracted from the momentum of the object traveling to the left.

It isn't so mysterious why Kinetic energy is not always conserved in collisions when you realize that lost kinetic energy turns into  heat or another form of energy (say sound or sparks).

>>1
My question is: if you start out with said reference frame, then won't the final momentum of the system be 0 also since the objects are stationary? What's wrong with my logic?
Nothing, your logic is completely correct. The final momentum of the system in that frame is zero, since the objects are stationary. This means that since momentum is conserved, in that reference frame the total momentum of the system is always zero at any point in time. Thus before the collision their respective momentums were equal but in opposite directions (in that frame) so as to add up to zero.

I wants lots and lots of some delectable pot!

Marijuana MUST be legalized.