Belief in "the world to come" is Rambam’s 13th Principle of Faith. The Talmud makes a claim that a Jew who doesn’t believe in "the world to come" can’t go there. I don’t understand how that can be a serious statement. Apparently, someone thinks you can trick Hashem into believing you believe something when you don’t, but I don’t think that’s possible. I’m very skeptical that there is any "world to come." I have not seen any evidence of it. Dawkins raised a very interesting point in regard to euthanasia. He pointed out the fact that the more religious someone was, the more likely they were to oppose it. He thought this was very hypocritical. I agree with him. If someone truly believed in “the world to come” they would help an old person in great physical pain get there, rather than pushing hard for a million road blocks causing them much superfluous suffering. Personally, I feel this life is probably the only life we have so I am completely opposed to euthanasia. We have to try to live as long as we can because when we go, that is probably it (for us). How do you reconcile a belief in the World to Come with a blanket prohibition on euthanasia?
As Maimonides writes, Judaism is clearly not pre-occupied with the world-to-come (to be with! God), but rather with this world, where we have free-will to be like (!) God. God gave each of us a soul, or a “spark of God”, with the potential to be Godly. By following His directions to be Godly (the mitzvot) found in the Torah, we realize our spiritual potential and live the objectively true and moral Godly ideals. For example, He created the world, and accordingly commands us in the very first mitzvah to be like Him and also create worlds, by having children. God “rests” on Shabbat, and suggests that we do so, as well. He constantly gives altruistically (without getting anything in return, for He’s perfect and doesn’t need anything!) and we should be similar “givers” as well. Accordingly, we don’t do the mitzvot in order to get into the world-to-come, but in order to be as much like God as possible in this world, which is obviously the most meaningful and highest moral and idealistic level anyone can achieve. Thus, the seriousness of the prohibition to murder anyone, including the mentally, chronically or terminally ill. Regarding the world-to-come, as I wrote, it's not the main point, but if you are interested in verifying it, you might enjoy the best-seller: “Life After Life”, which documents more than 100 cases of clinical death, which describes experiences very similar with those found in Jewish traditional sources. Rabbi Ari Shvat