Another of my favorite exercises: the one-legged squat, aka the pistol or pistol squat.
What is it? The pistol is a squat down on one leg, with the other leg held forward.
The pistol is an excellent test of balance and strength, and it can build your strength up pretty quickly once you start doing them. But there is one big problem with it - you need to be strong and balanced enough to do one before you can start knocking them out.
The simplest progression I've seen is to start with the Pistol Box Squat. Medhi over at Stronglifts has a nice article on using boxes to build up to an unsupported pistol. The short version is, you sit down to a box with one leg out, and then stand up from the box. The box ensures you go to the same depth on each rep, provides a safety net if you lose your balance and fall backwards, and also always you to train your strength up from its weakest point - a full stop at the bottom.
Once you've mastered the basic pistol box squat, you can move up to the free-standing box squat.
This isn't the only progression to the pistol, however. You can also look at the article on the pistol over at Beastskills. It provides another progression up to a pistol, as well as advanced pistol versions for those strong enough to knock off free-standing pistols with ease.
Why do I want to do these? Besides being a cool party trick, it's also a great single-leg strength builder. Practically all sports involve single-leg strength, so you can even up any discrepancies in strength between your legs with single leg work. While Bulgarian split-squats, lunges, step-ups, and sled dragging are all excellent, the single-legged squat provides a different challenge. Pistols also are great for when your access to external resistance is minimal. Get strong enough and balanced enough for a single rep and you can start using these for a handy no-equipment leg workout.
Plus, honestly, they're fun. Do one or two...once you start repping them out, you'll feel stronger and you'll enjoy doing them. Sure, the full pistol is hard, but you've got a couple ways to build up to it now. No more excuses not to at least try it!