I like to write long sentences, but people complain that I move from thought to thought in the same sentence, and that it ought to be split into multiple sentences. Although I'd like to correct this problem, I'm not sure how to define a complete thought. Can someone please define it for me? Thank you.
Err on the side of brevity. As a rule of thumb, short (but grammatically complete) sentences are preferable to long sentences because they are easier to read. If a sentence can be easily split into two, then you should usually do so. Where this would leave you with a very short sentence or a lack of context, it may be preferable to keep the independent clauses together and throw in a coordinating conjunction instead, but this should not be the default.
Another helpful rule of thumb is to count the number of commas and conjunctions (and, or, but) in a single sentence. Unless a sentence contains an embedded list, you should rarely have more than two or three of each in a sentence. For most sentences, you should have one or zero of each.
Finally, take into account stylistic considerations. If you are intentionally writing in a "stream of consciousness" style to evoke a particular creative effect, then run-on sentences are an entirely legitimate and appropriate technique.