I've been using an HSA since the beginning.

First thing to understand is that you fund your HSA with PRE-TAX dollars. Meaning, you don't pay income tax on that money. Right now the limit for a family is $6250 at least in my state.
Second, you can use HSA funds for many things that your insurance will not cover. Besides the obvious, (co pays, the portion of your bill that you have pay towards the deductible) you can use it for vision, dental, massage, prescriptions, medical devices, and even certain over the counter products. The lists are available online, and documentation is the key. Our medical insurance does not cover prescriptions, period, so I use the HSA to pay for those.

In a perfect world, what you pay into and use with an HSA would exactly match your co pay and out of pocket expenses, but in reality, with the things that aren't covered, you will probably run out of HSA funds before you spend your plan out of pocket maximum.
I think the only people who have trouble seeing the tax benefit are those who've had the gold plated kind of plans where they've never had to actually pay for much of the actual cost of medical care ( $5 dollar office visits, no copay, minimum deductible.