Kelvin's hydroelectric generator
en.wikipedia.org
en.wikipedia.org
*Solar panels I suppose are technically mechanical because they rely on a photon striking a surface.
There was also an article on HN about using osmotic pressure or something to generate electricity, basically an electron transport chain in reverse (I don't think I saved it...) I guess that's not as cool as Kelvin's thunderstorm, since it's basically just another chemical battery.
EDIT: Ah, never mind, it was just powering a turbine: http://news.ycombinator.com/item?id=435149
What about electrochemistry (i.e. batteries and fuel cells)?
Trying to think of others, I guess I would include triboelectricity and the piezo effect among the mechanical methods. A thermocouple isn't mechanical though unless you are going to argue that it relies on kinetic energy of atoms. Alpha and beta decay are non-mechanical; also, there are some schemes for direct conversion of energy radiated from a (hypothetical) fusion reactor in the form of charged particles into electric current without a thermal/mechanical intermediate step.
Does the EMP from a nuclear weapon count as 'generated electricity'? (Would that be considered mechanical?)
(several edits: I thought of more.)
It is cool.
esp. this bit see WEIRDNESS: really really gigantic generators