In 4 years of riding about 30,000 km a year in Europe on my Canadian plated bike, no-one has ever asked me to show anything other than a passport - and the requests for the passport have only been when going in and out of the EC, for example, in and out of the former Yugoslavian countries, or in and out of Switzerland.
Having said that, though, you still have the same obligation to have the papers and to produce them if asked as you would have in North America - the only difference is that you are expected to also have a passport. As mentioned above, passport controls at the border crossings have been eliminated, but you often will see police or customs officers at the side of the road within 25 km or so of a border crossing, just doing random spot checks. I think they are more concerned about locals moving more than their allowed quantity of cigarettes, liquor, etc. from country to country, not so much with visitors.
If you have not been in Europe before, do be aware that speed limits vary from country to country, and speed limits are normally NOT posted every half mile along a roadway, as they are in North America. Instead, you will see a single big sign at the border crossing advising you what the default speed limits are within cities, on secondary roads, and on expressways. Be sure to stop and take a look at this sign, because you won't see the information repeated once you are in the country. Also, be aware that in most European countries, the presence of a sign indicating the name of the town (e.g. "Chicago") is also the point where the speed limit changes from the default highway speed limit to the default city speed limit. You are expected to know this. Likewise, when you leave a town, the presence of an almost identical sign, but with the name of the town you are leaving crossed out, indicates that you may resume the 'out of town' speed limit.