Answer: Certainly: If you see a sharp in a measure then all the following notes of that pitch are sharped, until the end of the measure. If the composer wants the sharp to be cancelled before the end of the measure there will be a "natural" sign needed. An editor will often put in a "precautionary" natural even after the sharp was cancelled by the bar line, just to remind the reader that the sharp is no longer in effect.

The sharp applies only to that particular pitch - not to other octaves of that pitch. So if there's a sharp on middle C it does not apply to the C above middle C unless it is written in.

Be on the lookout for errors, though. Depending on the care of the editor, you will sometimes find a missing accidental (notated sharp or flat) in printed music.