I am a UK citizen and resident. Does my non-EU (USA) spouse need to apply for a special visa to travel in the EU for longer than 90 days in one block? We want to travel (cycle-touring) in the Schengen area for up to 180 days without working. Obviously she would normally get the 90 days as a US citizen, but do we need to register or apply for a visa to be able to stay beyond that period?
It's a difficult problem and I can't see any obvious solution.
Before I explain why, note that if your wife wasn't your wife but just a random US citizen, she most definitely could not stay more than 90 days in (most of) the Schengen area. She would have to qualify for a residence permit/long-stay visa for that and, in many countries, those have pretty onerous requirements and are not generally available for tourism. So, by default, the visa system isn't designed to allow it.
But your wife is your wife and there is no reason she should not be able to accompany you. Clearly, you have a right to visit several EU countries in turn and in principle your freedom of movement trumps any other rule. Article 3 of the Schengen Borders code even reads:
This Regulation shall apply to any person crossing the internal or external borders of Member States, without prejudice to:
(a) the rights of persons enjoying the right of free movement under Union law; […]
And article 2 explicitly defines “persons enjoying the right of free movement” as
Union citizens within the meaning of Article 20(1) of the Treaty, and third-country nationals who are members of the family of a Union citizen exercising his or her right to free movement […]
In other words, with a few minor caveats and as long as you travel together, the EU freedom of movement covers you and your spouse.
In practice, the system works in the following way:
If you visit for less than 90 days, your wife can enter visa-free under regular Schengen rules. If she could not (because her citizenship would not entitle her to visa-free visits), she should be able to get a visa easily merely by proving that she is your wife and travelling with you.
This “right of residence for up to three months” in another EU country is covered in article 6 of the free movement directive. Because of this, there are very few valid reasons to refuse entry and/or a visa to members of the family of an EU citizen (that's unlike the situation of other visitors who must in principle fulfil a number of conditions regarding the purpose and conditions of their stay).
If you intend to stay longer than 90 days, your wife would need some form of residence document. It's also easy to obtain, again by proving that you qualify for the EU freedom of movement and that she is your wife. The free movement directive also explicitly mention this (in article 9).
Even working is perfectly fine. It's actually easier to get a residence permit for your spouse if you work than if you don't (because then you don't have to prove you have sufficient resources and health insurance, only that you do have work). And if you qualify, your wife can work too, without restrictions.
Either way, you have a very strong right to travel in the EU and, indirectly, your spouse does too.
The problem, however, is that while the 90-day maximum stay limit applies Schengen-wide, residence permits/cards are still only valid for one country. There is no such thing as a Schengen long-stay visa or Schengen permit that would cover your wife's stays across several Schengen countries. And even if residence cards are theoretically easy to obtain, you will in practice need to provide an address, some documentation, and possibly wait 4 to 6 months to get one.
Technically, if you don't stay in any one country for more than three months, you would seem to be covered by article 6 of the directive. But that means your wife will eventually show up at the border with an entry stamp dating back many months in the past and border guards might have a problem with that.
Maybe you would be able to successfully argue that it's completely legal based on the logic I just exposed. At least, the most she would risk in this case should be a fine (“proportionate and non-discriminatory sanctions” according to the directive) because she had a right to be in the EU with you, she just failed to complete some formalities in time. So, unlike someone who overstayed a visa or stayed illegally, she would not risk a ban, removal or detention. But I have never seen an official source explicitly state that it was OK and dealing with the border guards could still be unpleasant.
If your wife does get a residence card somewhere, you have more flexibility. First, the time in the country that issued the card will not count towards the 90-day maximum stay. It means you could do something like 90 days in France (without formalities), 90+ days in Germany (under the cover of a residence card) and finally 90 days in Poland (because US citizens can stay another 90 days in the Schengen area after a cooling off period).
And while a residence card would not allow her to stay in another country than the one that issued the card longer than 90 days without registering, you could in practice cheat a little bit (there are no stamps when crossing internal borders and minimal risks; on exit, the border guards would see that she had a residence card for the relevant period and probably be happy with that). Finally, if your wife holds a residence card as “member of the family of an EU citizen”, she should not receive entry and exit stamps anymore so one more reason for border guards not to look at them.
The main problem with this approach is that you would need to find a home and stay put for a few months while waiting for the residence card (not only in the same country but in the same area, close to where you applied for the residence card) instead of completing your tour in one go.