I travel to Germany a few times a year. While there, I usually keep my passport in my hotel room safe but keep a picture of my passport page showing my photo and passport number in my wallet. I'm wondering if I were pulled over for a traffic ticket if my passport picture along with my drivers license is sufficient ID or should I always carry my passport with me?

You should be fine with your current approach. While German law requires you to have an ID, the law does NOT require you to have the ID with you at all times. With your passport and your paper copy you have enough data about you that in normal cases nobody would insist on seeing the original (Formally, if you don't have the original police would have the right to accompany you back to your hotel to check the ID).

In general, I've had to show my ID much less often in normal life (=when I'm not traveling by air) in Germany than in the US anyway, I can only remember one instance in the past 25 years where I was stopped and asked for my ID. This was part of a very large search for an escaped criminal, and I think even there the driver's license would probably have been sufficient.

I never had to show anything other than my drivers license and my car registration, so I think the copy of your passport would not even be necessary, but of course it would not hurt to have it either.

Technically if you are not EU citizen or German (or have a permanent residency permit for Germany or any EU state) you have to carry a valid ID (passport or national ID) with you at all times. If you are stopped by the police and don't have it, you will have to take them to place where you kept it immediately for verification. Technically they can book you for a offense similar to a misdemeanor, but most don't.

A drivers license is just that: a permit to drive. My GF blissfully used to carry her Swedish DL around on trips to Germany thinking it was enough. Since I have a migration background (as the Germans so kindly put it) living in Bavaria I'm often stopped, even when accompanied by my (ash)blond Swedish wife and by now well aware of the rules Luckily the German national ID is CC sized now and easily shown. I have a naturalized Indonesian colleague who confuses the police by saying he doesn't have his passport with him and that he would not go with them. After 2-3 round of arguing he just says because he has his German ID

I have been flying internationally between Germany and other Schengen countries about ten times this month and have not had to show my passport to any German police types or airlines this month.

As an ordinary US citizen visiting Germany, I am technically required by law to have my passport available when in Germany. However, there are some circumstances where technically such requirement may not necessarily be legal. It is easier to have the passport around if dealing with the police, although visitor passport loss/theft is a greater problem when the passport is on the move than when the passport is in a fixed location.

Not that I have ever been checked for ID internationally, and I know that this is not a 'legitimate' use of the card, but I just carry my US Passport Card and leave the Passport book in the hotel safe.

I know that it isn't valid for travel (except for land/sea from Canada/Mexico), but it might be 'good enough' in certain situations.