This is a question I get asked all the time and the answer is: it depends.
I know you're probably thinking that it's not a very good answer, but let me explain...
Coffee starts out as the seed of a cherry fruit from the coffee plant. The seed is dried out until its moisture content is roughly 12%. In its green form, the coffee bean is not much use for producing a cup of coffee. In fact the main flavour characteristic is grass!
So to bring out the coffee flavour, we have to roast the bean. When we roast it, the coffee bean undergoes changes in its chemistry that affect its flavour. Sugars are slowly caramelised, which means that sweetness decreases and the coffee becomes more bitter. Smoke is released along with the carbon dioxide so essentially the weight of the coffee bean decreases and its volume increases. It becomes less dense.
Caffeine, however, tends to stick around. It isn't affected by the roasting process and therefore remains in the same quantities throughout. Since during the roasting process the total volume increases and the weight decreases then if you're measuring coffee out by weight there is more caffeine per gram in dark roasted coffee than there is in a light or medium roast. However, if you're measuring your coffee out by volume (e.g. by using a scoop) then there is less caffeine per millilitre in darker roasted coffee.
So there you go. As I said, it depends on how you're measuring your coffee out.
p.s. A lot of commercial espresso blends contain a mixture of Arabica and Robusta coffee beans. The Robusta coffee bean contains a lot more caffeine than Arabica so an espresso blend containing Robusta will naturally contain more caffeine. This is also true for instant coffee, which is also made with the inferior Robusta bean. Cheaper, but definitely not as nice.
Check out our range of dark and medium Arabica roasted coffees available to buy online now.