The abstract concept of a "NAND gate" is useful.
There are a surprisingly large number of ways to implement that concept.
Each implementation requires (at least) 2 inputs, (at least) 1 output, etc.
One important characteristic is the "cascade property" so that we can have a whole series of more-or-less identical gates that produce the logically correct output when the output of one gate feeds into the input of the next gate in a long chain or tree.
Also, physical implementations require some sort of power source, often assumed but not specifically drawn on a logic diagram.

popular logic gate implementations

Some popular implementations:
* static CMOS
* dynamic CMOS
* TTL
* "transistor per input" integrated RTL
* electromagnetic relays
* wine club∞

non-destructive computing

Non-destructive computing, also called reversible computing, Charge Recovery Logic, or Adiabatic Logic, involves gates that use almost zero power.

When a computational system erases a bit of information, it must dissipate a theoretical minimum energy of kT ln(2) -- the von Neumann-Landauer limit -- where k is Boltzmann's constant and T is the temperature.

Most logic gates erase a bit of information for every logic operation.
However, there are a few logic gates that preserve every bit.
In theory these non-destructive logic gates could use far less power than the theoretical minimum power of bit-destructive logic gates.

"Reversible Logic"[3] by Ralph C. Merkle at Zyvex

RevComp - The Reversible and Quantum Computing Research Group[4]
has some nice photos of their reversible CPU.

"Introduction to reversible computing: motivation, progress, and challenges"
by Michael P. Frank 2005.
http://doi.acm.org/10.1145/1062261.1062324∞ essays∞

"Reversible computing" index at Isawiki.
http://en.isawiki.org/wiki/reversible_computing∞

other logic gate implementations

Some less famous implementations:

A few unusual logic gates are listed in the article
"Ten weirdest computers"[1]:
* Optical computing
* Quantum computing
* DNA computing
* Reversible computing
* Billiard Ball computing and domino computing
* Neuronal computing
* Magnetic (NMR) computing
* Glooper Computer: Andrew Adamatzky makes interfering waves of propagating ions in a chemical goo behave like logic gates. "The waves are produced by a pulsing cyclic chemical reaction called the Belousov-Zhabotinsky reaction."
* slime mould computers
* Water wave computing

A few more unusual logic gates that are apparently not quite weird enough to make that article:

* IIL integrated injected logic
* marble computing
* spool valves: David Cary has designed a CPU to be built entirely out of spool valves, and is still pondering whether to power the thing with traditional hydraulic oil pressure, water pressure, or air pressure.
* The [fluidic logic][2] gates have no moving parts, if you don't count the fluid moving through them as a "part".


(Is there an article on Wikipedia or some other wiki with a list of ways to implement the abstract concept of a "logic gate" ?)


[1]: http://www.newscientist.com/article/dn13656∞
[2]: http://en.wikipedia.org/wiki/fluidic_logic∞
[3]: http://www.zyvex.com/nanotech/reversible.html∞
[4]: http://www.cise.ufl.edu/research/revcomp/∞