If you have a low pressure gas where molecules are isolated from each other then the simple answer is that photons of the incorrect frequencies simply can't be absorbed very well. You can see this by shining broad spectrum light like from the sun or a tungsten lamp through the gas and seeing that fairly distinct narrow bands of frequencies will be missing corresponding exactly to the emmission spectrum of the same element. You can visually see this by splitting the resulting light through a prisim.

It is called the absorption spectra of elements. This is a well known and well studied phenomenon, it's taught to high school chemistry students often including a practical experiment. It has a lot of applications in analysis and astronomy.

http://www.dynamicscience.com.au/tester/solutions1/space%20science/absorptionspectroscopy.htm

The reason it can't like just go into the kinetic energy of the atom is that you need to conserve momentum amoung other things and if other molecules aren't around to take part in the interaction this just isn't possible.

When you have a more dense material you can get more much more interesting pathways however. A relatively simple one is that the excess energy goes into producing a phonon which is a quantum vibrational mode of a lattice, basically just heat.

However there are some really strange things that can happen with dense materials though. For example you can get crystals that take a photon and split it into two.