The character that the MySQL client program recognizes as a statement delimiter is . . . . . . . .

: → This option is incorrect. The colon (:) character is not recognized as a statement delimiter by the MySQL client program. It's not a standard delimiter in MySQL.
. → This option is incorrect. The period (.) character is not recognized as a statement delimiter by the MySQL client program. It's typically used as a separator in schema-qualified object names, such as database_name.table_name.
; → This is the correct option. The semicolon (;) character is universally recognized as the statement delimiter in MySQL. It signifies the end of an SQL statement and is required to execute statements correctly.
, → This option is incorrect. The comma (,) character is not recognized as a statement delimiter by the MySQL client program. It's used to separate values in a list or columns in a SELECT statement's column list.

Therefore, the character recognized by the MySQL client program as a statement delimiter is Option C: ;.