How many Israelites came out of Egypt with Moses?

The mature men were about 600,000 (Exodus 12:37), plus the 23,000 Levites (Numbers 3:39). To this must be added the converts (Exodus 12:38), and the women and children. Based on the ratio of firstborn to younger children (Numbers ch.3), it can be seen that the children were numerous. Estimates for the total number are usually given at two million or more.

Concerning the Exodus and archaeology in general, see:

Did the Exodus happen

Evidence of the Exodus

And the wider picture. Archaeology in general:

Archaeology and the Hebrew Bible

The Holy Bible records that there were 600, 000 males aged between 20 and 60. You do the math, there must have been somewhere between 2 1/2 and 3 million in total.

(Exodus 12:37)

"And the children of Israel journeyed from Rameses to Succoth, about six hundred thousand on foot who were men, besides children."

So you have 600,000 men and it's fair to assume an equal amount of women for a total of 1,200,000 adults.

There's no telling how many children each family had; so the number could be anywhere from 2 million people and up.

In addition, in the year following the Israelites' departure from the land of Egypt, G-d asked Moses to conduct a census, which concluded that there were 603,550 men over the age of 20 who were fit for military service. (Num. 1:1-46)

However, men in Israel were considered mature over the age of 13, so there were probably many more men than women. Also, it was Jewish tradition to have many children per family. Also, the amount of men did not include the multitudes who would have included foreign people, slaves from other nations, etc.

The Bible says that 600,000 fighting men were among the Israelites who left Egypt during the biblical Exodus. Donald Redford (Egypt, Canaan and Israel in Ancient Times) extrapolates from Numbers 1:46 to give the total number of Israelites who were said to have fled Egypt as 2.5 million, compared to the total estimated Egyptian population of only 3 to 4.5 million.

For more information, please see:
http://christianity.answers.com/theology/moses-in-history-and-tradition
http://christianity.answers.com/bible/the-book-of-exodus