One way is to use RegularExpression
str = "This is, my string number 5!";
reg = RegularExpression["[A-Za-z0-9 ]"];
StringJoin[StringCases[str, reg]] // InputForm
gives
"This is my string number 5"
The " " is for any space, and [AA-Za-z0-9]9
stuff is for alpha numeric.