What is a topic to research in the classroom?

If you are talking about doing empirical pedagogical research, your first step should be thinking about what sort of research project you can do in a feasible manner. For example, if you are a professor teaching a multi-section course, you can set up studies with students in 4 sections assigned to use one learning strategy and 4 sections assigned a different one and compare results. You need to be able to create two groups containing at least 40-50 people per group (more is better) to have useful statistical results.
If you do not have enough study subjects for statistical analysis (a basic rule of thumb is that N=50 is the minimum for significance), you will need to to some form of ethnography, watching and closely describing an individual learner or pedagogical method. 
You may be able to do historical research as well, doing something like looking through archives of syllabi for a given course and analyzing how they have changed over a 10 or 20 year period. 
 

I definitely recommend choosing a research topic that you are interested in.  If a bunch of topics sound equally appealing, choose the one that will be the most beneficial to your readers or the school.  Here are ten that I think are particularly interesting. 
Does teacher feedback actually help improve student learning?
Does homework improve student learning?
What types of homework are most effective for student learners?
Does the classroom seating arrangement have any effect on student learning?
Does the classroom seating arrangement have any effect on classroom management?  
Does listening to music while studying for tests and taking tests improve test scores?
Does technology improve student learning?  
Do male students perform better in math and science related courses than female students perform?  
Athletes technically have fewer hours to work on schoolwork; therefore, their grades and completion rates should be lower than students who do not participate in sports.  Is this true or is the opposite true?  
What type of learner are most students?  Visual, auditory, or kinesthetic learners?   Do teachers effectively balance all three teaching and learning styles?