How many research interests should be included in a statement of purpose/objective
Be as specific as possible.  Do not bluff.

Remember that admissions committees are looking for strong evidence of research potential.  One of the markers of that potential is a deep interest in your intended research area.  For that reason, it's important to describe your potential research interests in specific and credible detail.  Why are you interested in field X?  What specific problems are you interested in working on?  What projects have you done?  What papers have you read (or written)?

It doesn't matter all that much what you write about.  We know that your interests will change over time.  Nobody is going to limit you to the specific research topics you describe in your statement.  Your statement is at least as much a demonstration of intellectual maturity as it is a description of research interests.

Eykanal's observations are correct.  Most graduate school applicants "barely know what's being researched".  A list of buzzwords mined from faculty web pages is not credible.  You can't effectively describe what your interests are when you aren't familiar with the field.  But I disagree with his conclusion; just because it's hard doesn't mean you shouldn't do it.  Don't be most applicants.  Know what's being researched.  Don't be vague, and don't just list buzzwords.  Make yourself familiar with the field.

After you've done that, writing about your research interests is easy, because you actually have some.