Stalactites: StalaCtites are the granddaddy of speleothems. They form when that first drip of water leaves a bathtub ring of calcite as it falls. Drop by drop, the calcite collects, forming a hollow tube, or soda straw, of crystallized calcite. Soda straws are quite common up to about a foot in length, and (in other caves with the right conditions) have been known to grow to tens of feet. Usually, though, the tube becomes plugged, and the water flows down the outside of the soda straw, forming the icicle looking stalactite. A stalactite with water flowing on just one side may become a thin drapery blade or bacon rind.
Stalagmites: StalaGmites form when calcite laden water splashes on the floor. The shape of stalagmites depends on gravity (they are round tipped, whereas stalactites are pointy) and often have a splash cup at the end or otherwise resemble candles from the spatter of the mineral laden water. Stalactites stick tight to the ceiling; stalagmites grow mightily from the ground--a silly but very effective way to keep these two names attached to the proper formation.
Stalactites and stalagmites often grow in pairs, and sometimes grow together forming columns. But sometimes, they grow singly, or in very uneven sizes. Stalactites over water will not form stalagmites. A slow drip on a stalactite may deposit all its calcite on the ceiling and leave little to form a stalagmite. With a fast drip, or steady stream, little calcite may stick to the ceiling, but instead build up a large stalagmite.
Soda straws, stalactites, stalagmites and columns are called dripstone, because they are deposited by dripping water. Flowing water can also deposit calcite down a wall or across a floor. This is called (surprise!) flowstone. Water in a cave stream can build up flowstone, called rimstone dams, across the stream, as the tumbling action of the water shakes loose carbon dioxide (just like shaking a can of soda pop does) and causes calcite to be deposited. Rimstone dam pools are often good aquatic habitat.
Cave coral or "popcorn" is unusual in that it can be deposited either above or below water. If an area is uniformly coated with coral, it is a good bet that it formed underwater. Sometimes the water in cave pools becomes so saturated with calcite that it simply falls out of solution because of its release of carbon dioxide gas, and the inability of the water to hold any more mineral in solution at that temperature.
Helictites are crazily growing calcite structures, most often resembling snarled roots or potato sprouts. It is believed they grow as the result of capillary action, as the water seeps from the rock and is then pulled along through tiny, internal canals within the depositing crystal structure instead of yielding to gravity. Nearly freestanding speleothems called shields are supposed to grow in a similar manner, but along hairline cracks in the bedrock, instead of circular pores. The cave shield in the Onondaga Cave Rock of Ages room is one of only a few in the United States.