Ten years ago there were many different answers to this question. Caffeine content varied a lot depending on the coffee, and method of decafination.
Today, most decaf coffee contains only trace amounts of caffeine. The EU requires 99.9% of caffeine be removed.
The USA only requires 97%, but since modern decaffination processes result in almost zero caffeine. This doesn't seem to factor in to the equation.
Milligrams of caffeine per brew
Does decaf still wake you up?
Yes, while there is almost no caffeine in decaf coffee, the psychological effect of drinking it can still give you a boost in energy and mood.6
Personally, the first sip of coffee gives me an instant boost—even though the effect of caffeine isn't instantaneous.
It also seems that just the smell of coffee is enough to wake you up