MRAM (magnetoresistive random access memory) flips the magnetisation of a region 180 degrees relative to another permanently magnetised region to store a 0 or a 1. MRAM is nanosecond fast but if made too small and close together will "cross talk".
FeRAM (ferroelectric random access memory) use small external electric fields to polarize ferroelectric crystals. FeRAMs low energy requirement and speed advantage is offset by the requirement that every memory bit requires a space hogging capacitor.
PCRAM (phase-change random access memory) use laser light or current to change a materials structure. If the current pulse is long, the material orders itself into its crystalline state (a conductor). If the pulse is short, the material cools abruptly into the amorphous state (an insulator). These memory regions can be made quite small, but the downside is that the melting requires lots of energy.
RRAM (resistive random access memory) use high voltages to drive off or reabsorb oxygen bound within molecules like titanium oxide. When the oxygen leaves, it leaves behind holes in the crystal and excess electrons that are available for conduction. This process requires almost no electrical current, making them very energy efficient. Another exciting property is that RRAMs can represent more than a 0 or 1. They are able to adopt any number of values for their resistance (memristors) which could make them models for the analogue computational elements (synapses) inside the human brain.
Racetrack memory moves tiny domains of magnetism along wires. The domains are moved along the wire by a current and written or read when they pass sensor heads. If the wires can be coiled into 3 D, the memory per volume will increase several hundred times.
Source: New Scientist