Use -s and -N:
> id=`mysql -uroot -ppwd -s -N -e "SELECT id FROM nagios.host WHERE name="$host""`
> echo $id
0
From the manual:
–silent, -s
Silent mode. Produce less output. This option can be given multiple times to produce less and less output. This option results in nontabular output format and escaping of special characters. Escaping may be disabled by using raw mode; see the description for the --raw option.–skip-column-names, -N
Do not write column names in results.
EDIT
Looks like -ss works as well and much easier to remember.