I found this out when I first joined Ancestry.com. I had an offer for a short term membership and wasn't sure I wanted to stay on for more than the three month trial period. When I called in, the customer representative was very helpful. He told me that I could have him set the cancellation date for the end of the trial period and not have to remember to call back to cancel or to rest the account information to not automatically renew.
It worked great - at the end of the three months even though I had forgotten the date my trial would end my membership lapsed. By then, I was sucked in and signed up for another year (at a great discount, calling to renew was worth the hold time since they gave me a 50% discount AND World membership for free!). Since then I have decided that it is worth it to me to have the auto renewal.
But last year there was an interesting situation. Our credit card company changed our card number and I forgot to change it on the Ancestry site. My membership ran out in September, but I didn't notice. I could still access the site, do my research, update my online tree, get emails from other Ancestry users, etc. It was only when I got Family Tree Maker and tried to link it to my online tree that I had a problem.
I got two free months before that happened. Then because the representative felt bad about the 'inconvenience' he gave me an extra month free to make up for it. And there was a free month with the Family Tree Maker purchase. Now I renew in January.
To get the best deals and to pre-set the cancellation date you do have to call in but it does remove the worry about having Ancestry automatically renew when your budget can't handle it.