Will nonbelievers burn?
This is a very complex question, so bear with me.
According to Judaism, worthy gentiles do have a place in the next world (olam habah). All people must follow seven laws, and Jewish people must follow these laws and then some. The seven laws are:
Do not steal
Do not murder
Do not commit adultery
Do not blaspheme God
Do not worship idolatry
Do not eat a limb torn from a living animal
Establish a justice system to enforce the above laws
If a gentile (a non-Jewish person) sits in his kitchen all day doing crossward puzzles, that person has not done anything wrong, and goes to olam habah. But that person was not neccessarily a GOOD person, as doing crosswards all day does not compare to, say, trying to rid the world of slavery
. A person who is actively (as opposed to passively) good, gets a "higher" place in olam habah- as I understand it a place closer to God's throne. This is true for all people, Jew and gentile.
If someone does not obey the above laws, theoretically has no place in the next world. I'm not exactly sure of the extent of this, and the following is my understanding which may have no actual basis in anything besides my opinion.
Because God created us all differently, a kleptomaniac has very different tests that someone who would never dream of invading another's privacy. Accordingly, God will judge the act of stealing differently in each case. We each start off at our own place, and we each end at our own place. What matters is not the "finish line" but how far we've come. Here in this world we do not know where someone else has begun, and we don't know how close they are to their goal, and we are obligated to judge others favorably. So no-one can say who will "burn" or not.
There is also a concept called teshuvah, which literally means return but is taken to mean repentance. If someone does sincere teshuvah, the offending action is wiped from that person's slate. If it is a person-to-person sin, forgiveness must be asked and granted before teshuvah can happen, but if it is a person-to-God sin, the forgiveness asked and granted is part of the teshuvah process. This is a big factor for the next world, because even deathbed teshuvah can earn a person a place in the world-to-come. (On a side note, the sin still exists in the world, and there are still consequences of that action, but it is no longer on the record of the person who committed the act.)
So anyone can avoid "burning" if they so desire.
I hope this wasn't too rambly, and that it actually answered the question.