Yes we believe that everyone goes to heaven, and if you didn't accept the gospel here you will have a chance to do it there.

yes. we believe that they will go to heaven but there are different degrees of glory. celetial(being the highest), terrestial, telestial, and outer darkness(which we don't really thin anyone wil go to unless u deny Jesus to his face). so really we don't have a heaven and hell we have different parts of heaven.

What you\'re asking is a really broad question- probably broader than you realize. The short answer is yes. We believe that all good people will get some degree of glory in the next life, no matter what religion you believe.  
 
Here\'s the more complex answer. (Warning- this gets complicated.) There are three degrees of glory- celestial, terrestial, and telestial. Then there\'s Outer Darkness, but we don\'t talk about that much. To achieve the celestial kingdom, you must be baptised into the Church of Jesus Christ of Latter-day Saints, get married in the temple, and endure to the end- that is, keep the commandments and do your best to follow Christ\'s example. I\'m not entirely sure about the terrestial and telestial kingdoms, I just know that they are lesser degrees of glory. We believe that to get to Outer Darkness, you have commit an unpardonable sin, like denying God and Jesus Christ when you know they\'re real. But like I said, we don\'t talk about that much. We prefer to set our sights on the celestial, nothing less. The thing about being in the lesser kingdoms, though, is that you cannot progress. Those who achieve the highest degree of glory will be able to continue on, to inherit /all/ their Father hath. Those in the lesser kingdoms are \'stuck\', sort of. They can\'t progress, and stagnation is a form of damnation. I\'m not entirely sure what happens to them- I think they just kind of stay there. 
 
However! I have gotten ahead of myself. That\'s the last stage of life as far as we know it. There is more, before the three degrees of glory and after earth life. After you die, your spirit goes to the Spirit World. The Spirit World is divided, sort of, into Spirit Prison and Spirit Paradise. Those in Paradise are \'Mormons\' who have lived good lives and done all that they should have. Those in Prison are those who, for whatever reason, have not accepted the gospel. Either they didn\'t get the opportunity to in their mortal lives, or something. Those in Paradise do missionary work among thier fellow spirits, teaching the gospel. Here on earth, we do temple baptisms for these dead spirits, and they choose whether to accept it or not. 
 
Moving on. The Second Coming happens, Christ comes again, and the Ressurrection happens. There is a Melinneum of peace and prosperity, in which Satan is bound and Christ reigns. We believe that geaneology work will be done during this period, and that when we are ressurected our bodies will be made perfect. Then, at the end of the Melinneum is Judgement Day, and the three degrees of glory that I talked about up there -^- come into play. At least, that\'s as near as I can understand it, thanks to my seminary teachers. 
 
Oh look, a diagram! ^_^ Hope this helps. Diagram (for Coolness)Diagram (for Simplicity)

ok, we actually beleive there is more than just heaven and heck. we actually beleive there are 3 kingdoms, and then what is called "outer darkness" which is like heck.  
 
CELESTIAL KINGDOM: the first and greatest kingdom is the celestial kingdom. (kind of like the sun kingdom.) it is the greatest place ever, and only if you are a very good, and of are the right faith, (mormon) and have repented of ALL of your sins can you get there. (we also beleive that the celestial kingdom is broken in too ANOTHER 3 parts, and you have to be married in the temple to get to the highest of those 3 parts.)  
 
TERESTIAL KINGDOM: the second is the terestial kingdom. (kind of like the moon kingdom) you do not have to be mormon to get there. if you were a good, wonderful person, but maybe didn't repent of all your sins or something, you get to go to the terestial kingdom. the terestial kingdom is just about like earth. 
 
TELESTIAL KINGDOM: the telestial kingdom is the last kingdom. (it is like the star kingdom) it is worse than earth, but you dont deserve to go to heck!  
 
OUTER DARKNESS: another word for heck. (pretty much self-explanitory)

It all depends on how you define Heaven. 
 
As has been stated there are 3 separate Kingdoms of Glory that are referred to as heavens. So if you define heaven as these three kingdoms of Glory then it is more pertanint to ask who won't get in, not who will get in. The answer is only the sons of perdition will not obtain a kingdom of glory, ie. only the sons of perdition will not go to one of these heavens. Meaning that anyone who is not a son of perdition will go to heaven. 
If you define heaven as Exaltation then the answer is now. Only people who are baptized can get into the highest kingdom of Glory and only those sealed to their spouses can receive Exaltation. 
 
However, we do baptisms and sealings for the dead via proxy ordnances in the temple. Meaning if someone goes through life a non-mormon they will have the chance to become one in the next life. (a non-mormon is anyone who has not been baptized by God's authority). 
 
This means that ANYONE who lives and complies worthily with the law that they know and have recieved(ignorance is covered by christ), will have the chance to recieve baptism, and sealings and will have the chance to be exaulted. 
 
So even though some rice farmer who lived up to all the spirtual laws he knew, did not get baptized in this life, he will have the chance to recieve baptism by proxy and recieve exaltation. 
 
God is no respector of persons and wants everyone to have the chance to enter into his rest, if he sent us to a place where there is no hope of ever recieving the Gospel and then just dammed us to hell, how could he be just or merciful, and what would be the point.

LDS belief states that every thing God creates for our salvation is for our benefit, even hell, which we believe is remedial in nature. Eventually hell and death will yield up its dead and every knee will bend and every tongue confess Christ. It's not that "only Mormons" will be saved, but the fact that all will be of one mind and one spirit, and there will be no name tags. All ordinances for the good of man, like baptism, must be administered by legal administrators of God's Kingdom, be they ancient or modern. As Joseph Smith said, a man cannot be saved or damned in ignorance.

The simple answer is that God is just and merciful. No one will ultimately be denied a blessing for which he qualifies. He gives the opportunity to go to heaven to everybody and all who qualify will go there.

I know this question has already been answered but I just want to add my little piece. When I was little my told me just because I was mormon did not mean I was going to the celestial kingdom, and a catholic, atheist, budhist etc... wouldn't not go to the celestial kingdom(I know that's probably not gramaticaly correct)  
granted they comply with all of the stuff mentioned above which I really do not feel like repeating. Its something that's helped me strive to ensure that I treat everyone equally, Mormon or not.

LDS Cosmology is very complex and confusing even to members! 
 
To answers simply all people that have never seen God, Jesus Christ, the Holy Ghost, or an Angel of God and rejected God's divinity go to a Kingdom of Heaven depending on there faith and works no matter how bad they were in life all will be rewarded with there proper kingdom in heaven unless they reject God with a physical knowledge of his existence (like Satan) did.  
 
To explain the three kingdoms takes a lot of time so I will give a brief description and please not that all things are not known about the afterlife and will not be known in this life.  
 
Celestial Kingdom: Is made up of three degrees of glory. Only those who accept Christ and have the ordinances of salvation performed can enter this kingdom or Glory. The highest degree of the Celestial Kingdom is exaltation we become a god and can obtain the ability to have spirit children of our own.  
 
Terrestrial Kingdom: Those who never accepted Christ but lived good lives inherit this kingdom of glory. It is a lesser glory than Celestial and because of that these people can never dwell in the presence of the Father only the Son and Holy Ghost. Until the day of Judgement all translated beings (like Enoch, Elijah, Moses) reside here. 
 
Telestial Kingdom: Is where those who never accepted Christ and lived immoral or bad lives reside. They live in a lesser glory than the previous two kingdoms neither the Father nor the Son can visit here only the Holy Ghost.  
 
Outer Darkness: This is a place of no glory outside of Heaven. If is a place of wailing and gnashing of teeth. Satan and his angels as well as any who committed an unforgivable sin. Like rejecting God when visited by a heavenly messenger or committing murder after covenanting not to when you enter the Church of Jesus Christ of Latter-day Saints.  
 
This place is overwhelmingly filled with the fallen host of Satan's rebellion against God. Very very few people who lived on Earth will inherit this eternal spiritual death.  
 
Hope this answered your questions!

I\'m wondering if a person who receives baptism after death and chooses not to become a mormon as a result and continues to remain the religion they practiced when on earth, like Catholic for example, What level of the 3 main levels of heaven will they go to. According to all the previous comments, it looks as though it wont be the celestial.