In Bash 4:
To lowercase
$ string="A FEW WORDS"
$ echo "${string,}"
a FEW WORDS
$ echo "${string,,}"
a few words
$ echo "${string,,[AEIUO]}"
a FeW WoRDS
$ string="A Few Words"
$ declare -l string
$ string=$string; echo "$string"
a few words
To uppercase
$ string="a few words"
$ echo "${string^}"
A few words
$ echo "${string^^}"
A FEW WORDS
$ echo "${string^^[aeiou]}"
A fEw wOrds
$ string="A Few Words"
$ declare -u string
$ string=$string; echo "$string"
A FEW WORDS
Toggle (undocumented, but optionally configurable at compile time)
$ string="A Few Words"
$ echo "${string~~}"
a fEW wORDS
$ string="A FEW WORDS"
$ echo "${string~}"
a FEW WORDS
$ string="a few words"
$ echo "${string~}"
A few words
Capitalize (undocumented, but optionally configurable at compile time)
$ string="a few words"
$ declare -c string
$ string=$string
$ echo "$string"
A few words
Title case:
$ string="a few words"
$ string=($string)
$ string="${string[@]^}"
$ echo "$string"
A Few Words
$ declare -c string
$ string=(a few words)
$ echo "${string[@]}"
A Few Words
$ string="a FeW WOrdS"
$ string=${string,,}
$ string=${string~}
$ echo "$string"
A few words
To turn off a declare attribute, use +. For example, declare +c string. This affects subsequent assignments and not the current value.
The declare options change the attribute of the variable, but not the contents. The reassignments in my examples update the contents to show the changes.
Edit:
Added "toggle first character by word" (${var~}) as suggested by ghostdog74.
Edit: Corrected tilde behavior to match Bash 4.3.
