Generally Dry cells refers to standard and alkaline cells. SLA (Sealed Led Acid), and other 'NON-Spillable' batteries such as NiMh and NiCd can also fly. They need to be declared as freight.
Lithiums are a delicate subject, and the general answer is that Lithium Primary cells may not fly unless they are covered by a US only special category called life saving equipment. or have very tiny amouts of Lithium (less than 1 gram per cell) and can survive the UN 3090 testing, and are not classed as hazmat, and may fly.
In general a few CR123's will not have enough lithium to be classed as Hazmat. A pallet full of them is another story however. Brand name CR123's such as Energizer, Duracell, Panasonic, Sanyo are likely to have passed the requirements Private label products are are suspect.
Various types of flashlights do qualify, especially if they are FAA TSO-C85 compliant (which means they have been explicity approved for carriage on aircraft use).
There are DOT exemptions however for many smaller Lithium primary cells such as coin cells. Otherwise they are classed as HazMat.
This is what got the first shipment of RazorBeam HID lights into so much grief. They were undeclared Hazmat.
Li-Ions can only travel as carryon, they may not fly as checked luggage or freight under ATA rules. US Carriers are not bound by ATA rules however, and within reason, may be transported by freight if properly declared on a carrier certified for Hazmat transport (I believe only Fedex is). IN general Li-Ions up to about 55 watt hours can travel as carry on (that covers cells phones, PDA's, laptops etc). Get beyond about 55 watt hours, and it becomes technically illegal to transport them by air, period, end, stop except as life saving equipment.