long term visa and or residency visa

What is your home country?

I am an American but in order to travel Europe for an extended period of time I would apply for residency in either France, Italy or Spain. We are retired with the income needed to qualify. I am wondering about the ability to travel freely for an extended periods of time of more than 90 days outside of the country I eventually get a residence visa from.

For less than 90 days, you do not require a visa. For longer, you do. Keep in mind that there are tax consequences with any long term visa. If you get a long term residence permit for France, you'll have to start paying French taxes.
The visa waiver rule is 90 days out of ANY 180 day period. And you don't have to go home, just not be in the Shengen treaty zone.

No. If you apply and are granted a long-term stay visa the 90-day rule does not apply. That is the whole point! Your home country really doesn't care how long you are gone as long as you keep paying your taxes according to the law! :) You can certainly travel around while "living" in another country on a long term visa. Currently there are no border checks between Schengen countries so that isn't an issue.
You will need a home base in France since a long-stay visa requires you to register with the police wherever you are planning to base yourself in France.
Here is the link to my local French Consulate with all of the information about applying for a long-term visa. It isn't a complicated process just a lot of paperwork and, eventually, an interview. Make sure you have your ducks in a row, so to speak, for your interview. Several people on this forum have posted as to the importance of making sure that everything is perfectly in order. Otherwise you'll be sent away and have to make a new appointment.
There are different layers of French taxes for expats staying there for an extended period of time. You need to consult with a tax attorney who knows about such things to find out what will be true in your case. The US federal government and the government of the state in which you live also have certain requirements. Each US state is different regarding payment of taxes while living overseas...some will make it easier to stop paying state taxes while others make it extremely difficult.
There is a great magazine called "Living in France" which comes out every month or two. It's aimed at British citizens but has lots of good information in every issue. It covers the practical aspects of living in France and gives a pretty good picture of some of the requirements. I buy it at Barnes&Noble and it's also online. It's a fun read!

I think the question the poster is asking is if they, as a US citizen, get a long term or residential visa from France, is there any problem if she stays in other Schengen countries for more than 90 days in 180.
The "home country" she is talking about is the country she has the long-term visa for (France).

I think the answer is yes. France doesn't mind how long you stay out of France, so long as you stay in France long enough to be still counted as a resident, and you pay your taxes. But you must still obey the limits for other countries.
Your French resdence permit acts as a tourist visa for the rest of Schengen - but not a work or residence permit. If you fly from London to Berlin (for example), you need to show your passport AND French residence permit, then they won't bother to check if you have exceeded the 90-day limit, as it doesn't apply.
But if you want to spend more than 90 days in Germany you will need a German visa. But as there is no passport checking between France and Germany so long as you are not working that limit is hard to enforce.

To get a definative answer you should ask the French consulate when you apply for your visa.

Here is a link to a web site where a couple moved to Portugal and obtained a residency visa. They give very good information on what they had to do, http://noparticularplacetogo.net/

Having just gone through this process myself.... It is not for the faint-of-heart nor casual traveler. It took us several months just to get the appointment to apply for a visa at the Italian consulate.

Just to get the visa you have to have a lease on a place to live, FBI background check, copies of everything financial you can think of, letters from banks, etc. The visa only gets you into the country. Then you have to apply for residency, another series of hoops to jump through. It took us 8 months from making the appointment for the visa to actually getting our permit to live in Italy.

To maintain residency, at least in Italy, you have to live here at least 6 months of the year. To me, that means maintain a residence, but you might consult an immigration attorney about that. If you stay 183 days or more, you are subject to Italian tax law.

We are never asked to show our permesso when we travel. Our U.S>passport is all anyone wants to see and no one asks us how long we've been anywhere, even when we leave the Schengen.

thank you all so much, I was getting conflicting information. sorry it wasn't until after I asked the question that I figured out an easy way to ask it. indeed I was wondering once I have a residency visa in one country if I could freely travel outside that country without worry to the time I would be gone. I will look into all the info you gave, I know it won't be an easy thing but at least it is doable. thanks again.