Non-Mormons go to heaven

The LDS church teaches that non-Mormons go to heaven. For starters you have Joseph Smith's vision where he saw Alvin in the Celestial Kingdom. The Lord told Joseph Smith,

7 Thus came the avoice of the Lord unto me, saying: All who have died without a knowledge of this gospel, who would have received it if they had been permitted to tarry, shall be heirs of the celestial kingdom of God;

8 Also all that shall die henceforth without a knowledge of it, who would have received it with all their hearts, shall be heirs of that kingdom;

9 For I, the Lord, will judge all men according to their works, according to the desire of their hearts.

10 And I also beheld that all children who die before they arrive at the years of accountability are saved in the celestial kingdom of heaven.[1]

Which heaven you wind up in is dependent on the depth of your salvation.[2]

Here is even a group of LDS Mormons discussing this.
http://www.askamormon.com/do-non-mormons-go-to-heaven.html

Non-mormons going to heaven has been a part of Mormonism for over a century.

I’ve always taken it as a given that Mormonism’s view of the afterlife shuffle has always been more universalizing than most of the other alternatives. Our formulation of heaven intuitively accommodates for the varying levels of understanding people can achieve in this life and in the spirit world: instead of a binary — heaven and hell — we have glories of heaven. So, we can safely say that although most people aren’t Mormons, most people won’t go to “Hell,” or at least, not the kind of Hell that many non-LDS religious people want to posit for nonbelievers of their religions. Regardless of people’s disagreements with the particulars of exaltation for the celestial aspirants, things actually look pretty good for the rest of us non-celestial people. [3]