Dangling one's prepositions is a very easy grammatical mistake to make, and one that I am often guilty of making. Sometimes restructuring your sentence merely to not leave a little word hanging would be ridiculous. I find, therefore, that I rarely notice dangled prepositions.
Except, there are certain instances wherein I do. You see, sometimes to get rid of that final preposition, you would have to go through the process of moving your sentence around, and it might come out so garbled as to not make sense. But other times, one would merely have to drop it off. And that is where I both notice it, and am annoyed by it.
For example "Where's it at?" is one that I hear quite frequently. In thinking about this particular ill wording, I discovered something that I find interesting: when I say "Where's it", it sounds odd, or wrong, and I find myself wanting to add "at". When I say "where is it", it sound clumsy and stumbling to add the same "at". Which lead me to the conclusion that our ears (or at least mine) are tuned to a lyrical quality in our language that leads us to desire a certain number of syllables in some sentences.
So, if you find yourself dangling a preposition, look for a contraction you use, and uncontract it.