Having been an apartment renter and now currently a landlord, I've been on both sides regarding the issues of pets and rentals. One must keep in mind that each rental situation is different, each tenant is different, each landlord is different and each pet is different.
Landlords have no-pets clauses in their rental agreements to protect further damage to their rental property. Some landlords have stipulated pet-clauses, such as higher security deposits or limits on types and/or quantity of pets. In reference to reptiles, some landlords may not have a basic understanding or have a phobia.
The best case is obviously to find one that accepts pets. If so, make sure that is specifically written into the rental agreement, and not performed verbally. However, be aware that in cases of month-to-month rental agreements, landlords can at their discretion issue a 30-day notice to alter the rental agreement to exclude pets.
However, in some cases, landlords are specific in the type of pet allowed onto their property. Learn what kind of limits there are. If your type of pet is excluded, there is no harm in inquiring the reasoning. Perhaps the landlord may just need to be educated.
Finally, when there is a definite no-pets stated, you can still inquire. You can explain what pet you have. If the animal is enclosed, describe it's habitat. Landlords are primarily concerned with property damage and liability to the other tenants. Some may regard pets as an additional burden to land lording. It doesn't hurt the situation to inquire and explain matters to the tenant. If it's a definite "no-pets", then it's best to look elsewhere.
I personally wouldn't advise on sneaking pets into a situation where it's clearly stated "no-pets" in the rental agreement. Firstly, you would be clearly violating the lease; in this case, even if you are in a rent-control environment, you will still face the penalties. The landlord can react in several ways. There's the "3-Day Quit" where you receive a letter stating that you have to remove the animal or vacate the property. There's another situation where they can just give you a 30-day notice to vacate the property. Once you have violated the agreement, you have basically very little alternatives. If you're fortunate, the landlord may choose to work with you; in that case, offer your full cooperation.
Landlords need "full" access to the property, in cases of emergency. Landlords have the right to enter a unit without notice in cases of emergency. Typically, they should provide you with a written 24-hour notice. Changing locks can be a violation of your rental agreement.
Check the legalities of owning your animal in your area.
Renting with Pets - The online resource for rental managers and pet owners from the Humane Society of the United States.
Pets OK, L.A. - The weekly newsletter for pet-friendly rentals in the Los Angeles area.
TenantNet - The online resource for residential tenants. This site focuses on New York City and New York State, but information from other areas is also available.
petswelcome.com - A fantastic web site with listings of hotels, motels, apartments and other destinations that are pet friendly. They also have an Info Xchange board for posting information about your pet and/or travel, information about how to travel with your pet, and much more!