There are positives and negatives to owning a duplex over a single family residence. A duplex allows you to rent out one side helping to reduce the financial burden your mortgage payment puts on you.
When qualifying for a mortgage in a Duplex, you can try and qualify as an owner occupied property if you will be living in one of the units. This may get you a loan with a lower interest rate as well as reduce the amount of down payment if any that may be required.
While buying a duplex may make more sense with the thought that you can rent 1 unit and live in the other unit you must remember that you will need to keep it rented, to a responsible renter, to gain a benefit over a single family home. This can sometimes prove to be a tough task; that is, getting a renter in there that pays the rent on time and keeps the unit clean and in good condition. You will also be responsible for maintenance of the unit you are not living in (along with the unit you do live in too). There will be items that will need to be fixed and possibly replaced, every time a renter leaves you will most likely have to go in and clean the carpets, possibly apply a fresh coat of paint, fix anything broken, etc... So therefore, just keep in mind that many more responsibilities come up with a duplex as opposed to a single family house.
If you decide to rent out one side and live in the other you will benefit from being an onsite landlord. You have an extremely lower probability of your tenants damaging your property when you are there.
Owning a duplex has several tax shelter opportunities. Some of these include being able to depreciate one-half of the duplex, and deducting the interest on the mortgage for both sides of the duplex.
Before purchasing a duplex, be sure to consider the resale potential of the property. Traditionally it has been more difficult to sell a duplex than a single family residence.