I use rechargeable Li-Ion for all my daily carry flashlights (yes, multiple - what can I say?!) But you have to buy a light that is designed to use the higher voltage. I am talking from the AA-size battery perspective. I use the 14500 rechargeable Li-Ions 99% of the time. My fallback to that are the Eneloop rechargeable NiMH's. Third fallback is Alkaline.

I only have one CR123 light (weapons light on my shotgun). For that, I use regular primary CR123's. For that use - very short and sporatic use (testing mostly) - I think primary lithium cells are the best.

If you are considering rechargeable CR123's, realize that there are DIFFERENT VOLTAGES available. Make sure you get something compatible with your flashlight. Also, if you have two rechargeable Li-Ions in series you sure as heck better make sure they are the "protected" kind. Otherwise you are at risk for fire and smoke. Better than two Li-Ion CR123's (I forgot the model designation for these) in series, I would recommend ONE 18650 cell that replaces both. Again, make sure your flashlight can handle the additional voltage.

The rule of thumb for rechargeable Li-Ion's is, if your are going to buy a cheap charger (the UltraFire for example), get GOOD batteries (e.g., AW brand, etc). If you are going to get cheap batteries (UltraFire, etc.) get a GOOD charger. I personally use an UltraFire charger for Li-ions, but for batteries I always use the top-notch AW brand protected cells.