I have been practicing this piece (The Stars and Stripes Forever) for a while. On the first note of the second measure of the second line, there is a natural sign. I have always understood accidentals not to affect notes outside of the current measure. If so, why is there a natural sign on the C while the key is F Major? Is this a mistake, or an obsolete practice (this is from 1897)? If the natural sign were not there, would the C be played as a C#?
The natural sign next to the C is a "courtesy accidental". It is there only to make it absolutely clear to the player that the C is not to be sharp.
It is correct that an accidental only carries through the bar, and thus that the one here is not necessary. But were it not there, though the note would be a C-natural, it would be easy upon sight-reading to play a C-sharp instead.
The practice of courtesy accidentals is still very common. A composer will include accidentals such as these to clear any confusion that may arise, and in so doing aid the performer's reading.
EDIT: The one exception is when a note with an accidental is tied (with a slur) over to the next bar. In this case, the note will keep the accidental.