string - How to trim whitespace from a Bash variable?

I would simply use sed:

function trim
{
    echo "$1" | sed -n '1h;1!H;${;g;s/^[ \t]*//g;s/[ \t]*$//g;p;}'
}

a) Example of usage on single-line string

string='    wordA wordB  wordC   wordD    '
trimmed=$( trim "$string" )
echo "GIVEN STRING: |$string|"
echo "TRIMMED STRING: |$trimmed|"

Output:

GIVEN STRING: |    wordA wordB  wordC   wordD    |
TRIMMED STRING: |wordA wordB  wordC   wordD|

b) Example of usage on multi-line string

string='    wordA
   >wordB<
wordC    '
trimmed=$( trim "$string" )
echo -e "GIVEN STRING: |$string|\n"
echo "TRIMMED STRING: |$trimmed|"

Output:

GIVEN STRING: |    wordAA
   >wordB<
wordC    |
TRIMMED STRING: |wordAA
   >wordB<
wordC|

c) Final note:
If you don't like to use a function, for single-line string you can simply use a "easier to remember" command like:

echo "$string" | sed -e 's/^[ \t]*//' | sed -e 's/[ \t]*$//'

Example:

echo "   wordA wordB wordC   " | sed -e 's/^[ \t]*//' | sed -e 's/[ \t]*$//'

Output:

wordA wordB wordC

Using the above on multi-line strings will work as well, but please note that it will cut any trailing/leading internal multiple space as well, as GuruM noticed in the comments

string='    wordAA
    >four spaces before<
 >one space before<    '
echo "$string" | sed -e 's/^[ \t]*//' | sed -e 's/[ \t]*$//'

Output:

wordAA
>four spaces before<
>one space before<

So if you do mind to keep those spaces, please use the function at the beginning of my answer!

d) EXPLANATION of the sed syntax "find and replace" on multi-line strings used inside the function trim:

sed -n '
# If the first line, copy the pattern to the hold buffer
1h
# If not the first line, then append the pattern to the hold buffer
1!H
# If the last line then ...
$ {
    # Copy from the hold to the pattern buffer
    g
    # Do the search and replace
    s/^[ \t]*//g
    s/[ \t]*$//g
    # print
    p
}'