I agree with others that it's likely how you're accessing the elements that is the problem. Quoting the file names in the array assignment is correct:

FILES=(
  "2011-09-04 21.43.02.jpg"
  "2011-09-05 10.23.14.jpg"
  "2011-09-09 12.31.16.jpg"
  "2011-09-11 08.43.12.jpg"
)

for f in "${FILES[@]}"
do
  echo "$f"
done

Using double quotes around any array of the form "${FILES[@]}" splits the array into one word per array element. It doesn't do any word-splitting beyond that.

Using "${FILES[*]}" also has a special meaning, but it joins the array elements with the first character of $IFS, resulting in one word, which is probably not what you want.

Using a bare ${array[@]} or ${array[*]} subjects the result of that expansion to further word-splitting, so you'll end up with words split on spaces (and anything else in $IFS) instead of one word per array element.

Using a C-style for loop is also fine and avoids worrying about word-splitting if you're not clear on it:

for (( i = 0; i < ${#FILES[@]}; i++ ))
do
  echo "${FILES[$i]}"
done

I agree with others that it's likely how you're accessing the elements that is the problem. Quoting the file names in the array assignment is correct:

FILES=(
  "2011-09-04 21.43.02.jpg"
  "2011-09-05 10.23.14.jpg"
  "2011-09-09 12.31.16.jpg"
  "2011-09-11 08.43.12.jpg"
)

for f in "${FILES[@]}"
do
  echo "$f"
done

Using double quotes around any array of the form "${FILES[@]}" splits the array into one word per array element. It doesn't do any word-splitting beyond that.

Using "${FILES[*]}" also has a special meaning, but it joins the array elements with the first character of $IFS, resulting in one word, which is probably not what you want.

Using a bare ${array[@]} or ${array[*]} subjects the result of that expansion to further word-splitting, so you'll end up with words split on spaces (and anything else in $IFS) instead of one word per array element.

Using a C-style for loop is also fine and avoids worrying about word-splitting if you're not clear on it:

for (( i = 0; i < ${#FILES[@]}; i++ ))
do
  echo "${FILES[$i]}"
done