Best answer to date: Both...

The ~consensus is that our sun will eventually reach a red giant stage
and
then move on to a red supergiant stage, after which it will very
gradually
become a white dwarf. This last stage will last for many tens of
billions
of years, as it slowly cools off. And no, it will not ever go
supernova.
It is not nearly massive enough for any type II SN event, and for a
dwarf to
go type Ia SN, a second or companion star is needed in fairly close
orbit, to send lots of material onto the dwarf, to push it over the
Chandra-
sekhar mass limit, ~ 1.3 Msol. One site that covers some of this is

http://en.wikipedia.org/wiki/White_dwarf

Cheers.