For myself, based on a week in the area last year, I'd say -

Chenonceau

Chenonceau

Chenonceau.

But if pressed I'd say, because they are all quite different from each other -

Chenonceau (plan all day there)

Chambord - because it is huge, much bigger than the others

one of the others to make up the numbers; maybe an unusual one like Beauregard, or the history at Amboise, or Blois for the sound and light show if you like that sort of thing, and to show how you can shoehorn a big chateau into the middle of a city.

I second the choices of Chenonceau and Chambord but if you have have any interest in gardens/grounds I would add Villandry as the 3rd. The chateau itself is not that spectacular but the gardens are!

It may help you in further trip research to know that the word usually used to describe most of these places is "chateau", not castle. Most are not "really" castles, if you're thinking of castles of an earlier time.

My vote goes to Chenonceau too – douze points!

To my opinion the outside of Chambord is not to miss, going inside can be debated as the interior is somewhat empty unless you really want to see that double helix staircase.

Château d’Amboise (as the town itself too) is nice and worth a visit in combination with Leonardo da Vinci’s grave and his last residence nearby Clos Lucé.

I liked my visit to Azay-le-Rideau, but agree with the gardens of Villandry.

Some reading before going to the places makes the visit more involving, like the intriguing story of Chenonceau, the rivalry between Chaterine de Medici and Dianne de Poitiers, and not only that.

Chaumont, anyone? The interior is fully decorated (unless my memory is failing me) and it's a beautiful building. One of the most "Disney-esque" castles of the Loire.

If you are a gardener, in addition to Villandry you should consider Chaumont. The garden show they have every year is spectacular.

Another vote or three for Chenonceau and the gardens of Villandry.

I also found the chateau in Amboise more interesting than I had expected -- especially for its views from above the river.

I liked Chaumont, and it's also perched high, but I honestly can't remember the view down -- but it must be a nice view as well.

The At a Glance listing at http://www.ricksteves.com/europe/france/loire applies Rick's rating system to the most popular choices, taken from his France guidebook.

I will also second Chenonceau and Chambord, as they are so different that it's great to see them both. We also did Cheverny, which is interesting b/c the family still lives on the 3rd floor and it's been maintained better than most (which are refurbished). But you don't get to go into a lot of the rooms and just stand at the door to look in.

We also hit Blois on the way down to the Loire from Versailles and that was interesting to see because it was so much older and different than the the chateaus.

Azay le Rideau is currently being renovated and about 2/3 of its exterior is currently covered in scaffolding, so you can't see the "fairy tale" exterior described in the book. It is supposed to last about 18 months total, I believe (two different phases).

1: Loches ; there are three castles in one here, a beautifully maintained one where Joan of Arc came to plead, an old fortree to explore, and a burned down one with just the skeleton in place.

2: Chaumont-sur-Loire : frankly this is our favorite castle ever... absolutely perfect! Castle, gardens, restaurants, etc.

3: Azay-le-Rideau: tears to my eyes it's so beautiful inside and out.

If you are there for the European heritage days when privately owned castles are open to the public for a weeked

5: Le Guy Pean : Up in a deep valley, snooty family but cool place!

6: L'islette (twin to azay-le-rideau) : Very beautiful setting!

You'll be amazed how many castles/ manors you'll see as you drive around, ones not on a map because they're private home and hotels now.

I love visiting Chenonceaux and Chambord. They are very royal and full of history.
Villandry is ok + pleasant and a stop on Rick Steves' tours.
Some of you have mentioned others of which I am ignorant and shall look into.

I like to look at the chateau listings in "Ouvert au Public."
The Grandmere often still lives there. My son as a young teenager stayed in one belonging to the family he was with.
Again the history of why they exist at all fascinates me.
Emile Zola's historical novel "Germinale" of the coal mines and the people who lorded it over the mineworkers is just an example.
(also saw the movie but cannot remember the exact title, English subtitles)

As to your question, definitely the 2 chateaux (C & C) mentioned by many posts. But I might want to do some research into the other not-so-known ones mentioned. I certainly shall.

Azay-Le Rideau is surrounded by scaffolding,might not be worth a stop.
Mike

Another worthwhile feature of Blois is that it consists of four historically and architecturally distinct wings around a central courtyard, from 15th to 17th century. You can learn a lot in a small place. And, as Nigel said, it's in the middle of a fair-sized city instead of out in the country or spanning a river or such. Wouldn't be my first pick (I'm with the Chenonceau crowd) but might be in my top three.

And I agree that you can get "chateau'ed out" after three or four. Don't know how long your Loire visit will be, but you could check out wineries, the city of Tours (not on the RS list but many like it), the walls around Angers, and the troglodyte caves west of Tours. And, for a completely different experience, the Zoo-Parc Beauval near St-Aignan, supposed to be among the best zoos in Europe.

Chambord and Chenonceau would be most people's first 2 picks.
Then it's a toss up for me between Villandry, Château d'Azay-le-Rideau and Ussé.
Look for yourself here ...http://www.frenchmoments.eu/top-10-most-beautiful-chateaux-of-the-loire-valley/