Yes and No...
There are some conditions attached to this answer...
First of all every non-Muslim, be they Hindu, Christian or Jewish... mainly people who are supposed to be worshippers of God (Allah) alone… monotheistic. If they adhere to their book, its commandments and do not worship anyone but God alone. Yes they will go to heaven… that is the more common belief in Islam.
But the problem is that these books and teachings had a time attached to them and that was until the next book or teaching arrives. Or if the original teachings were still intact.
We know from Hinduism that they have added a lot more deities into their religion and very few people actually read and follow their holy book. Similarly many of the Christians have started the concept of trinity, to the extent that many people worship and hold Jesus (May Peace Be Upon Him) with higher regards than God himself. Thus going against the very first commandment of Christianity.
Jewish people though they still believe and worship the one God, have had a lot of interference in their book by men of religion who Allah describes as men who have sold their religion in liu of money… as well as making permissible things forbidden and vice versa. Plus with the coming of Christianity and Islam, the Jews were supposed to believe in these two prophets but they denied them. Despite both of them being mentioned in their holy Books.
So we can say that most of the non-muslims who followed the books of god, who practiced their religious as described by their respective prophets and books will surely go to heaven. But with the coming of new books, new revelations and prophets, of them that did not believe in the new commandments will not go to heaven.
"O you who have been given the Scripture (Jews and Christians)! Believe in what We have revealed (to Muhammad PBUH) confirming what is (already) with you,"
Most of the people from other religions, including many Muslims… Do not follow their religious teachings as they were revealed and thus will go to the hell fire.
There is an exception for people who do not follow any religion but do believe there is God and he is the all-powerful and he alone is to be worshipped. People who Allah describes as on the religion of Abraham (Ibrahim) known as Hanifa. These will be allowed into heaven… subject to having not come across any of Gods texts/messages/messengers/teachings etc. If they have and denied them… then the above waiver is not applicable.
Verily, Allah forgives not that partners should be set up with him in worship, but He forgives except that (anything else) to whom He pleases, and whoever sets up partners with Allah in worship, he has indeed invented a tremendous sin.
Lastly what is to happen to people who have never heard of Islam, the message never reached them and they died in that state. Though I do not have any solid proof to reference. In Islam it is understood that they will be pardoned and allowed to enter heaven.
Anyone who does get to know about Islam and God but refutes it and does not worship God or takes partners with him will enter hell fire… be they Muslims or not.
''Verily, those who disbelieve (in the religion of Islam, the Quran and Prophet Muhammad (peace be upon him) from among the people of the scripture (Jews and Christian) and Al-Mushrikoon (polytheists) will abide in the fire of Hell. They are the worst of creatures''
The Prophet (peace and blessings of Allah be upon him) said, ''By the one in whose hand is my soul, no one of this nation, Jew or Christian, hears of me then dies without having believed in that with which I was sent, but he will one of the people of the fire'' Narrated by Muslim, 153
Hope this has answered your question :)