Many people do believe that they are one and the same (obviously) and as I said before, I don't want to offend anyone. So if anyone reading this believes that they are, feel free to ignore everything I say.
The evidence lies in Jesus' own words. If Jesus and God are the same person, they would have to be equal. However, as Jesus said in John 14:28, "The Father is greater than I am."Jesus also explained that there were some things that neither he nor the angels knew, but that were known only by God. (Mark 13:32) If Jesus and God were one and the same, how could God know something that Jesus could not? Jesus also prayed to his father "let, not my will, but yours take place." (Luke 22:42) Who was Jesus praying to if not someone superior to him? And again, if they are the same person, how could their wills differ? And it was God who resurrected Jesus from death, not Jesus himself. (Acts 2:32)
Scripturally, then God and Jesus are two distinct individuals. Some scriptures have been used to show evidence that the opposite is true, though, which would be contradictory. A closer look at their meaning reveals the true meaning though.
One such scripture is John 10:30, "I and the Father are one." On the surface, this does seem it could support the notion that they were one entity. However, several chapters later, Jesus showed what he meant by his being "one" with the Father. Looking at John 17:21,22 we see him in prayer. He asks God that his disciples "may all be one, just as you, Father, are in union with me and I am in union with you, that they also may be in union with us ... that they may be one just as we are one." Jesus was praying that his disciples would, not become a single entity, but be united in thought and purpose, as he and God were. The Greek word used for "one" is neuter, literally "one thing", indicating oneness in cooperation. It's the same word Jesus used at John 10:30 to describe his relationship with his Father. It's also the same Greek word Jesus used at John 17:21,22.
In the interest of keeping this from getting too long, I'll just mention one more scrupture sometimes used in support of God and Jesus being one. In John 5:18, it says that the Jews wanted to kill Jesus because "he was also calling God his own Father, making himself equal to God." However, it was not Jesus saying he was making himself equal to God. He defended himself against this false charge in the next verse. (John 5:19) "To this accusation Jesus replied: ... ‘the Son can do nothing by himself; he can do only what he sees the Father doing.'" Jesus showed that he was not equal to God and, therefore, could not act on his own initiative. It's hard to imagine someone equal to Almighty God saying that he could "do nothing by himself.", especially when comparing Daniel 4:34,35.