I believe/ I do believe

do字有加強語氣及肯定既意思~~
i believe我相信
i do believe我非常相信

I agree with most of the other responses

I DO believe is to emphasize that you TRULY believe

it's like the difference between:
I go to school
and
I do go to school (you might say this when you parents say "gee you're always so lazy that you can't even make yourself go to school")

do是加強語氣

基本上無分別

加個do字只是加強語氣

無特別意思

I believe = 我相信
I do believe = 我一定相信