How important is tamping coffee for an espresso machine I observe that coffee servers (I refuse to use the term barista) will apply pressure to the coffee grounds using a variety of methods and pressure. This seems to vary wildly and I'd like to know how important is this? Is there some general rule of thumb when it comes to recommended pressure?

My thoughts were that the fineness mattered the most for espresso machines and that reasonable enough pressure when tamping is enough but what do expert's use and believe.
Tamping is one of three key controls you have over the espresso brewing process; The others are dose (the amount of coffee used) and grind coarseness.  Together, they allow the coffee machine operator to produce a puck of the correct density and consistency through which the pressurized water can be pushed through.

While techniques vary, the "rule of thumb" is to apply roughly thirty pounds of force evenly across the puck; however, the key is consistency.  Keep your variables the consistent and you'll be able to dial in the best end-product.

I've been able to pull great shots using anything from just the weight of the tamper itself to my full weight pushed onto a puck, keeping all of the other factors where they needed to be to create the correct puck density.

See this video below for more detail: What is the Right Way to Tamp?