Does any average kind of decaffeinated coffee have zero or very little caffeine in it?
We have yet to invent a process that removes 100% of the caffeine. When drinking decaf, the important question to consider is how likely you are to feel the effects of the trace amounts of caffeine that are left. That brings us, as most things do, back to the beans.
Arabica has (on average) only half of the caffeine that Robusta contains. Now let's say you have a bag of Robusta where 80% of the beans have 1 - 2% of their original amounts, and 20% of the beans have 15% of their original amounts. Drop by drop, a shot of Robusta is much more likely to keep you awake or elicit other natural responses to caffeine than an identically-sized shot of Arabica.
But let's take that into context and not pick on Robusta so much - the single shot we mentioned might only contain 20mg of caffeine in total, meaning you wouldn't notice the effects any more than you would notice effects from the Arabica. The point is, you could, so if you want to avoid caffeine, go with the milder bean and faster extraction.
Just goes to show, when you're talking about the characteristics of any coffee, the bean is pretty paramount - it can change the answer to any question completely in many cases.
According to Wikipedia:
Decaffeinated drinks contain typically 1–2% of the original caffeine content, and sometimes as much as 20% [Decaffeination] is repeated from 8 to 12 times until the caffeine content meets the required standard (97% of caffeine removed according to the international standard, or 99.9% caffeine-free by mass as per the EU standard).
A controlled study of ten samples of prepared decaffeinated coffee from coffee shops showed that some caffeine remained. Fourteen to twenty cups of such decaffeinated coffee would contain as much caffeine as one cup of regular coffee. The 16-ounce (473-ml) cups of coffee samples contained caffeine in the range of 8.6 mg to 13.9 mg. In another study of popular brands of decaf coffees, the caffeine content varied from 3 mg to 32 mg. An 8-ounce (237-ml) cup of regular coffee contains 95–200 mg of caffeine, and a 12-ounce (355-milliliter) serving of Coca-Cola contains 36 mg.
In contrast, your average dark chocolate bar sees 12 mg of caffeine per serving.