Mostly agreed with a post above except for a little expansion and small correction:
However, at about 150% of a solar mass, another threshold is crossed. Things get much more complicated, with hotter interior temperatures, more elaborate phases of nuclear conversion and much faster evolution. And the Chandrasekhar limit has been crossed: the star must ultimately blow up.
Stars from the 0.08 M
sun minimum threshold (to form a star at all) up to stars of about 1.25 M
sun have a core temp. < 16 million K and fuse H to He
mostly by the Proton-Proton Chain process. Our sun's core is ~14.5 million K. Above 16 million K, the predominant H fusion process is the CNO Cycle. Here we are talking about
Main Sequence stars, before He fusion starts at much higher temperatures; approaching 100 million K. He burning is by the Triple-Alpha process, and all three of these fusion reactions are nicely explained at:
http://www.shef.ac.uk/physics/people/vdhillon/teaching/phy213/phy213_fusion3.html
At 1.5 M
sun mentioned in the quote above, the star would have a core temperature of about 19 million K (and the CNO Cycle), but
the mention of the Chandrasekhar limit and its result (supernova) is not correct. Here's why, and I'm posting it because the "Chandrasekhar limit" has been mentioned here on PF forever but often in the wrong, or mis-understood, context.
When Chandrasekhar was on the boat to England in 1930-x (?) he calculated the effects of gravity against electron degeneracy pressure and came up with the famous limit of ~1.44 M
sun above which
any mass, including White Dwarf stars, would further collapse. In most cases we know of today this would be into a neutron star. He also calculated another "limit" of ~3.2 M
sun above which any mass would collapse again; black hole.
But, these masses were not, and had no direct relation to, a star's initial, or main sequence mass.
As main sequence stars evolve, and no two are exactly the same, they go through various fusion reactions dependant upon core temperatures and various degrees of expansion into giants / supergiants, etc. Almost all star types go through some process of mass ejection, mass loss CME's, etc. even including mass blasted away by way of a supernova (either type).
It is only the mass of the stellar remnant (core) after mass ejection that we need to consider as to when Chandra's Limit(s) would apply. As a general rule, which I happen to hate, a star of less than about 5 M
sun would either never form a core of >1.44 M
sun or would eject enough mass so that any remaining core would still be less than that limit. A lot of this was posted in the recent topic about Planetary Nebulae.
Stars from ~ 5-10 solar masses (main sequence) would have a remaining core of 1.44 or more and collapse into neutron stars. Above about 10, there would usually be enough mass in the remaining core to go supernova, and the core after even that blast would still be over 3.2 solar masses and do the black hole thing..

Most books for this purpose usually just state an original, main sequence mass of 8 solar masses or less which would end up as white dwarfs, not neutron stars.
[Edit]:
"General rules" don't cut the mustard. From one site we get:
"
The stars that eventually become neutron stars are thought to start out with about 15 to 30 times the mass of our sun. These numbers are probably going to change as supernova simulations become more precise, but it appears that for initial masses much less than 15 solar masses the star becomes a white dwarf, whereas for initial masses a lot higher than 30 solar masses you get a black hole instead." [End edit]