Kevin's talking about connotation and denotation again. Today, it is "reconsider" and "consider again". They totally mean the same thing except that they don't.
To 'consider' is to think about. Maybe it is thinking somewhat deeply or a little more thoroughly, but it is pretty innocuous - just general thinking about a subject.
To 'consider again' means that you have thought about something and, having finished that, you decided to think about it some more. It usually implies that you still have the same belief you originally held, but that you are wanting to confirm that your belief is accurate.
To 'reconsider' means the same thing, but the implication is the opposite. You reconsider something when you think that your original beliefs were incorrect.
Obviously, using the phrase with the proper connotation is important if you want to express yourself clearly (or you could avoid it by not using either phrase, but that would be stifling). But be aware that 'reconsider' and 'consider again' are not total opposites of each other. Get a feel for the nuances of them (just like you should for any word you would use).