I am renting a house in Arizona and the landlord is not providing blinds or any window coverings. Also, there is no rack in the stove there are leaks under the sinks and the biggest prolem is the shower in the master bathroom leaks into the family room. I have notified the owner and he has done nothing we have been here for 3 months now. I do not used the shower in my bathroom as it looks like the ceiling will cave in do to water damage. My question is, is the landlord responsible for the blinds or window coverings and a rack in the stove? Also what do I do about the repairs?

Window coverings may not be the landlord's responsibility. If it is, then cheap blinds is all they have to supply. The rack in the oven is a different story. But the leaks are the big issue. Especially if you have to pay the water bill.

Az law is not very tenant friendly on this:
Housing > Landlord and Tenant Rights and Responsibilities > Arizona Residential Landlord and Tenant Act (http://azlawhelp.org/articles_info.cfm?sc=24&mc=3&articleid=25)

If the cost of the repairs are less than half the rent, then you can advise the landlord that he has 10 days to make the repairs or you will hire someone to and deduct the cost from the rent. So you will have to get an estimate of the repairs first. Or if the problems affect habitability, you can cite breach of lease and move. The site I linked to has details on this.

Take pictures, document your complaints to him in writing, and give your rent to a lawyer to hold in escrow.
When I lived in MA, window shades were required to be supplied by landlords, but I don't know about AZ.
A house that includes a stove would be expected to include a stove rack.

Where there curtains or blinds in the house when you looked at it before you rented it ?

Was there any discussion about them.

When I did my rentals, some had curtains, some did not. I can not find a reference in your area where it is requried.

Is there any rack, bottom or anywhere that allows oven to be used. If not I feel argument can be made for that. ( although they are fairly cheap)

Was there not obvious water damage to home from the showers when you inspected it ?