The amount of rent due each month as printed on the lease agreement is the enforceable amount for the duration of the agreement. Once that agreement expires the landlord can renew the lease at a higher rate (the market level) if he wishes. Landlords commonly place clauses in leases describing this process.
In the case of a month-to-month agreement, the landlord may have legal authority to increase the rent with proper written notice (usually 30 days) since there is no long-term contract regarding the rental.
A lease is an enforceable contract. The landlord cannot go back on the agreement after both parties have signed and decide to charge another rate. However, some residential leases may allow the landlord to terminate the lease at any time for any reason, after which he may offer a new lease at a higher rate.
It's your responsibility as a tenant to read and understand the lease. Check the lease thoroughly to make sure it does not have any unusual clauses regarding rent increases at the landlord's whim.