What's the difference between I think and I believe when it  comes to expressing opinions?
Are they interchangeable?

Let's put them both into a sentence and see if the meaning is the same or different. 

"I think the Earth is flat." means that you have considered the idea of the Earth being flat, round, square, or held up on the backs of elephants, and in your opinion, the Earth is flat. In this scenario, there is a possibility that you might be willing to think about it again.

"I believe the Earth is flat." means that you don't need to consider the idea, you already know the answer that you agree with. In this scenario, you are less likely to be convinced that your opinion in not correct.

That's a good question Camilo.  When I think of the phrase "I think" and notice how i used it in the beginning of this sentence, I think it expresses my ideas about whatever it is I'm thinking about.  In this example, What I think "I think" means.  Wow, now doesn't that sound confusing!  If I were to say "I believe" what president Obama said in his speech, in this context it reflects a strong conviction and "belief" of what the president said.  Contrarily, I could say "Now, I believe president Obama is telling the truth."  With this particular inflection, it reflects a bit of uncertainty.  So I agree with the others that these two phrases could be used interchangeably, but I also interject that the meaning could be interpreted differently based on the tone and inflection.  Hope this wasn't confusing.

To answer the question, yes, most of the time they're interchangeable. But I would also agree with Andi that we may use them in different ways, for example, "I think" can sound less confrontational or definitive than "I believe". 

President Obama uses "I believe" a lot in his speeches. It can sound more authoritative, or carry more weight, than "I think".

In reality you can use "I think" and "I believe" interchangeably.

"I think" is your own opinion.
"I believe" is what you know about someone else's opinion.