Most, but not all, lenders require property taxes and insurance to be put in escrow especially if your down payment was less than 20%. For certain mortgages backed by a government program, you will not have the option of paying taxes and insurance on your own.
However, if you have the option of paying these expenses on your own, think carefully before doing so. Generally, these expenses are only paid once or twice a year. People who choose to pay on their own sometimes find it difficult to put aside the money themselves and are unable to make payments when the bills come.