This is entirely up to you. It is perfectly reasonable to ask your house sitter for a security deposit to insure against any damage to your property. If you would prefer the peace of mind a security deposit can bring, make this clear when you first contact potential house sitters. The amount is negotiable but shouldn't be more than the equivalent of a month's rent for a similar property in the area.
Please note that you should never request a security deposit to be sent to you before the assignment (especially over email)! To avoid the possibility of house sitters worrying about being defrauded, money should only change hands between house sitters and you when all parties are together at the property just before the you (the home owners) are about to leave.
Our house sitting agreement has a 'security deposit lodgement' form included in it which you can use to help make the whole process more organized and straightforward.