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[BeefontheBone]

Going back a bit here, but I thought I'd fill in what some of these are often used for (in no way exhaustive - for longer lists, look them up on wikipedia...)

Α α Alpha - many things, including alpha particles in the physics of nuclear reactions, and regularly used in mathematics. For a start, Greek letters are generally used to denote ordinals in set theory/logic.

Β β Beta - beta particles in nuclear reactions (essentially loose electrons)

Γ γ Gamma - the factor 1/sqrt(1-(v*v/c*c)) in relativistic calculations, where v is the relative velocity of an object to the observer, and c the speed of light. Upper case gamma is used as the symbol for a collection of formulae in logic, notably in the standard proofs of Godel's Incompleteness Theorems, among others.

Δ δ Delta - often a very small quantity, especially the small change in something in the calculus. Upper case is used similarly (in slightly different contexts), and to denote sets in logic.

Ε ε Epsilon - in analysis, a small number.

Ζ ζ Zeta - Not frequently used in mathematics, probably because it's hard to write . The first thing that comes to mind is the Riemann Zeta Function, an obscure function defined by the father of analysis, about which there exists a problem the solution to which would net its finder a million dollar prize.

Η η Eta - viscosity in fluid dynamics.

Θ θ Theta - usually an angle, esp. in polar coordinates.

Ι ι Iota - I actually can't think of a use for this one, probably because it's so similar to the romance i.

Κ κ Kappa - frequently used in analysis and topology. Denotes a particular measure of the curvature of a surface (whose name escapes me at present).

Λ λ Lambda - statisticians use this a lot, as do other mathematicians, including analysts.

Μ μ Mu - coefficients of friction, IIRC, are denoted by mu.

Ν ν Nu -
Ξ ξ Xi - not used a lot in maths (again, hard to write )

Ο ο Omicron - too much like o

Π π Pi - well, it's the constant ratio of the circumference of a circle to its diameter, for a start. Upper case pi is used for a repeated multiplication (in the same way that sigma is used for summation)

Ρ ρ Rho - density, usually.

Σ σ ς Sigma - upper case often denotes a repeated summation. Lower case is used for particular functions in many contexts, amongst other things.

Τ τ Tau - The Golden Ratio (more commonly, phi). Torque. Also a lepton in atomic physics.

Υ υ Upsilon - another one I can't think of a use for
Φ φ Phi - phi and psi usually denote general formulae in formal logic. Phi is also often used for angles in polar coordinates, and the Golden Ratio (also tau).

Χ χ Chi - chromatic indices in graph theory. There's also a statistical distribution called the "chi-squared" distribution.

Ψ ψ Psi - a general formula in logic

Ω ω Omega - Many many things. For a start, omega denotes angular velocity, and is used to denote the first infinite cardinal (equal to the number of integers).