I think flu touched on many of the things you need to know/consider. I don;t think there is one single answer because of all the factors.

I think there are three basic scenarios (with various options within each) to consider, and lots of issues to sort out with each.
You’ll have to consider each under your particular circumstances (e.g. value of home, size of mortgage, your income, your marital status, etc).

1. Buy it yourself as a second home.
Let your parents live in it free or have them separately give you cash gift payments less than the annual gift tax limits (could be as much as ~52K per year as of 2012. $13 K gift from each parent to you and $13 K gift form each parent to your spouse, assuming you are married.

In this case, if your combined mortgage balances on your primary (of you own one) and the secondary are less than $1 Million, then you can generally deduct the mortgage expense on both. However, there is that darn AMT. And second home interest is probably on the chopping block or further limited in the current fiscal cliff environment.

2. Buy it as a Rental property.
You could treat it as a rental property and rent to your parents. The consequences of this depend on several factors:
– If the rent is too low, there are tax consequences in terms of how much loss you can take. – Annual losses on rentals phase out as your income approaches 150K (joint).
– Would you want to hold this as a rental long-term (e.g. after your parents pass) or would you want to move there eventually.

3. Purchase jointly with your parents.
This might allow them to deduct the interest payment , if they are making them. But it depends on what tax bracket they are in, relative to you.
The downside here are all the estate issues you’d have to deal with.

All of these assume you are financing. If you are paying cash, I would simply buy it as a second home in your name.