Is it true that there was a time when Jews believed in the existence of several Gods instead of just One? Somebody told me that there was a time when they even worshiped different Gods - even after Moses. Is that true?
Throughout the Bible, many Jews keep veering into idolatry, such as the examples seen in Yaakov's answer. (Fascinatingly the whole idolatry thing comes to a screeching halt right around the Jews' return from Babylon to Israel around 2500 years ago. The Talmud says there was some "itch" that idol-worship seemed to "scratch" that dissipated then.)
But the "proper Jewish belief and practice" was clearly in one God -- just that lots of Jews kept having problems following it, apparently.
This is clearly depicted in numerous locations in the bible. To name a few major pagan cults, you have the Golden Calf worship in Exodus, Baal Peor worship in Numbers, and Baal worship in Kings.
You have to make a distinction between believing in the existence of multiple gods (which is clearly accepted in the Tanach - see God on the Egyptian Gods) and worshiping them. Only when the Jewish people turned to idolatry did they actually worship other Gods, but they were certainly 'aware' of their 'existence', and believed them to exist. This is why Aseret Ha'dibrot says "You shall have no other gods…" - that is, you will worship no other gods, and not "there are no other gods".
However, I believe it was accepted by the Jews that God was the King/Lord/Greatest among all the deities. I'm reminded of Ramban's (I think) commentary where he instructs on how to call on the deities that are in charge of celestial bodies to curse people. Source is commentary on D'varim 18:10-11
See this wikipedia article on monolatry for a more complete explanation.