Depends. There are three types of point mutations (changes affecting just one nucleic base pair):
Substitution - the wrong nucleic acid is present. Most of these are silent, but they can result in the wrong amino acid being coded for (Sickle Cell is one of these). In a worst case, they result in the stop codon being found in the middle of a sequence so the protein is truncated.
Deletion - one nucleic acid is removed. These are bad, and cause a frame-shift. The protein is most likely completely changed.
Insertion - an extra nucleic acid is inserted. Also a frame-shift, see above.
Other larger mutations can have similar effects.