My long-time partner and I want to buy a house together. What problems are involved? Is this a good idea? 

Certainly it is a good idea, especially in today's favorable real estate climate. 

When you decide to buy property together, your marital status doesn't have immediate implications. This changes if the relationship ends.

People often believe that couples who live together for seven years are automatically married by common law. But laws governing domestic partnerships differ by state, county and city.
Quoted in the New York Times, attorney Craig Davitian says the best advice for all unmarried couples buying a home is the same: sign a property agreement with your partner.

It sounds obvious, but before putting anything into writing, have an honest discussion with your partner about your respective visions for handling property, real and personal, if the relationship ends.
Make an agreement that keeps working even if the relationship doesn't.

Then visit an attorney and have your plan written into a property agreement. The process is easy if you and your partner talked through everything. It will only cost a few hours in lawyer's fees.

Anything can be encompassed in this agreement, but it's crucial to at least address the following items:

1) What percentage of the property is owned by each person? This is particularly important if one person has a larger financial stake in the property payments or down payment.

2) How will the title or ownership be described in official records?

3) What will happen to the property if the relationship ends? Will it be sold and the proceeds divided or can one person buy out the other?

4) Who gets one partner's share if the property is sold after his or her death?  Does full ownership go to the survivor, or do the partner's heirs get a share?

Look at the agreement  like an insurance policy. You hope you will never need it, but if you do, you'll be glad to have it.