What is the brightest star in the sky besides the sun?

The star with the brightest apparent magnitude other than the Sun is Sirius, alpha Canis Majoris.

Neither of them is particularly noteworthy on an absolutemagnitude scale; Sirius is only about 25x brighter than the Sun, and only appears so much brighter in the night sky than other stars because it's so close (astronomically speaking, 8 and a half light years is pretty dang close).

The brightest specific star currently known has the rather unmemorable name of R136a1 and is nearly nine million times brighter than the Sun, but is so far away ... about 165,000 light years, in the Lesser Magellanic Cloud ... that it's not visible to the naked eye.