They will give it back to you, but usually mark it to indicate that it is no longer valid. In the USA, I believe they generally mark it with the words CANCELLED and punch a couple of holes in it.
Looking at my expired passport - it has a big CANCELED stamped in some odd color of reddish pink purple on the signature page and two holes punched through the front cover. Since ours were renewed, the stamp also has NEW APPLICATION with the month/year entered and whether a fee was paid or not. A canceled US passport is quite obvious.
My old passport has been hole-punched with "Cancelled" in both official languages. They did that when I applied for the new one, as my old one was still valid for a few more months. You can't miss it--it's hard to even turn the pages.
For those following this thread: I successfully traveled with two US passports via a 3rd European country from Russia to China. The airlines asked to see both passports to ensure that I had both the Chinese and Russian visas and the airline representatives didn't seem surprised at all. In passport control it seemed they couldn't care less where I had come from or what passports I had been using as long as I had a valid visa.
You can get two passports from the US if you write a letter explaining that you need two to be able to visit various countries. Some countries will not let you visit if you have certain other country's stamp in the passport. Some middle eastern countries will not let you visit if you have an Israeli stamp. Israel will not allow their citizens to visit certain countries they consider their enemies and may deny someone back into Israel after they have a stamp of a number of other countries.
You might want to check with each country's rules of entry and exit, before deciding whether you need 2 passports and then also to know which to use when.
In most countries, if you get a new passport, as Ivanovich did, it invalidates/replaces the old passport. You can't use the old passport anymore. But a couple of times I've gotten a new passport while I was living abroad. In that case, I had to keep my old passport because it had my visas in it, which you have to show at customs.
Besides, old passports make great souvenirs.
[ Edit: Edited on 13-Oct-2010, at 22:02 by madpoet ]
Dual nationals owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries. Either country has the right to enforce its laws, particularly if the person later travels there.Most U.S. citizens, including dual nationals, must use a U.S. passport to enter and leave the United States. Dual nationals may also be required by the foreign country to use its passport to enter and leave that country. Use of the foreign passport does not endanger U.S. citizenship.Most countries permit a person to renounce or otherwise lose citizenship.