Yes, you should flush it. No, you probably haven't. Here's when, why, and how much of a difference it makes.
Sediment collects in the bottom of every tank-style water heater. In Connecticut, where much of our water carries some mineral content, that sediment builds up faster than you'd think. Left alone, it insulates the burner from the water, drives up your energy bill, and shortens the life of the tank.
The standard recommendation is to flush a tank water heater once a year. In practice, most homeowners have never flushed theirs — and the tank shows it. If yours has never been flushed and it's more than a few years old, flushing may not help much at this point, and it can sometimes reveal existing damage.
For a newer tank, annual flushing is genuinely worthwhile. It extends the useful life by 2–5 years on average and keeps efficiency high. For a tankless unit, an annual descaling service is required by most manufacturer warranties.
Can you do it yourself? Yes — the steps are well documented, and if your unit is under 5 years old, it's a reasonable DIY project. Just be careful with hot water and know where your shutoffs are.
If you're not comfortable, or your unit is older, have a plumber do it as part of an annual service call. It's inexpensive and pays for itself in equipment life alone.