How long tenant can stay without agreement?

There is no time limit. However it is always better to renew the agreement. The tenant cannot claim any ownership rights irrespective of the length of his stay.

While giving rent to a family you have to prepare and should give and every 11 months you should make a agreement and preiodically you can raise the rent 

if maintenance also you can take some amount from the family who is staying in the house 

and they have no right to claim your property in any manner even after they stay more then 15 years and if they go to court to claim the property has they are staying more then 10 years the case may run more than one year finally the case will be dismissed as he is only tenant and he has no right in claiming the property he is staying

while drafting the rental agreement note all the points what all to be kept and take a lawyer decision and draft it and lawyer will prepare it for you 

A tenant can continue in a building he has taken on rent till he is evicted by proper legal method..  Untill the expiry of agreement he is a contractual tenant, and he and the building owner is bound by the terms of agreement thereafter he is statutory tenant and both the parties get rights as the Rent Control Act of the state gives them.