OK, the simplest example first: Since you are a German citizen, you and your wife could retire to with only minor "inconveniences." I believe she would still need a visa and residence permit - but that should be fairly straightforward to obtain. For any other EU country, you could retire there, and then your wife would be eligible for the "simplified" process for a "close family member" ing their EU national spouse. The process does vary quite a bit from one country to the next - the EU only specifies that there shall be a "simplified" procedure available. In your own EU country (i.e. ), you're subject to the same immigration laws and procedure as anyone else wanting to obtain a visa for your non-EU spouse.
As far as taxes are concerned, you are always considered "tax resident" in the US, no matter where in the world you live. And you would be considered "tax resident" in whatever EU country (including ) where you were living. does claim the right to tax your US SS pension. But you would have to declare your "worldwide income" to both and the US and then take advantage of various procedures in the tax treaty to avoid double taxation. The same pretty much holds true in most other EU countries - other than the matter of which country gets to tax your US SS pension. Normally, the US gets first dibs on that.
On health care, you might run into some issues. Health care cover is mandatory in most EU countries and again, the precise details on how and when you can sign up for the national cover vary from one country to the next. Normally, you'd have a means of transferring health cover from one EU country to another if you had been living and working in another EU country, but coming from the US that isn't the case. Someone with specific information on will chime in here, but I believe it may be difficult, if not impossible for someone without prior EU cover to enroll in the German health care system. But stay tuned - someone will have more details on that.
Anyhow, a very quick overview. I'm sure folks will fill in the details.