What properties limits the maximum and minimum masses of stars ?

Answer 1

while these answers are correct on the minimum mass necessary to sustain hydrogen fusion (Look up "L" stars), they miss the boat on why stars cannot be more massive than a certain amount.

As you may know, as you look at more and more massive they become brighter much faster than you might expect (for instance a star ten times as massive as the sun may be about 3000 times brighter!). They get a little bigger, but mostly they become more luminous per area. At some point they are so luminous that atoms on the surface are lifted off in a stellar wind quite rapidly. Extremely massive stars evaporate quite quickly, reducing their mass and thus their luminosity until they are not evaporating so quickly.

Wiki has an OK treatment of this concept which was originally applied to the problem of how quickly an object can accrete material.
http://en.wikipedia.org/wiki/Eddington_limit

The actual luminosity limit is lower, because the effective cross section of the gas to photon interactions is dependent on opacity. For pure hydrogen the electron scattering cross section is the one to use, but as soon as you put in a few heavy elements (heavier than helium) it goes up very quickly for even small concentrations. So far, amongst non-primordial stars, the most massive ones we seem to see are around 100 times the mass of the sun. 60 is the lowest upper limit I have ever heard and 120 is about the highest.

Early first generation stars made from pure primordial hydrogen, helium and a dash of lithium would very likely only be limited by the opacity used in the Eddington limit. I estimate these guys would top out around 200 solar masses.

Answer 2

Well, on the minimum side, there must be enough mass to create a gravitational field strong enough to crush the matter down into the center of the would be star with enough force to ignite a fusion reaction. It is the reaction which makes a star shine as hydrogen is converted into helium and energy is released.
On the maximum side, the only limit is the amount of matter in the vicinity of the star. Red giant stars like Betelgeuse for example are so large that they make our sun look like a BB next to a beach ball.

Answer 3

Mass, mass, mass. The minimum mass an object would have to be in order for it's own gravity to cause nuclear reactions within it be around 5 times Jupiter's mass.
Jupiter is actually a GREAT example of a "star" that didn't have enough mass to actually start shining.
I don't beleive there is a "maximum".