For me, my main lens used to max out at 28mm in the days of DSLR. At one point in time, I had a 10.5mm fish-eye (16mm equivalent) and while it's a fun lens to use, I barely shoot more than 100 frames with it. Since the introduction of the Panasonic LX-2 compact digital, I've grown to like a slightly wider view of 24mm focal length. A slightly wider view allows me to capture more details than a 28mm focal length while not being too wide and difficult to compose.
Here are some ways I find the 24mm focal length to be very effective. Shooting landscape with a 24mm means that it is relatively easy to capture the whole environment like land, sea (or water), and sky in the same shot. The trick is to find an angle (be it higher, lower, more left, or more right) that works for each shot. For example, if the sky is interesting and colorful, compose for the sky.
Recently I rode on the Shinkansen (Bullet Train) and wanted to capture a scene that conveys the mood and the speed of that trip. With a 24mm lens, it's wide enough to cover the entire window view, including reflection from internal lighting. So here's that one shot taken at 1/2 second, handheld.
Experimenting with composition, architectural scenes are also ideal for 24mm. Like landscape, there's just 'enough' to fit into a frame. Not too much, and not too little, in my opinion.
Because of what can be included in one frame, it's not too difficult to compose to illustrate depth and motion.
People, in general, can be a little more challenging to shoot with a 24mm lens because the details can easily distract from the people itself. Every now and then there are shots that, for me, works with those details like the photos below. Be it the colorful paints, the sloping hill, or the sizzling tofu which contrasts with the calmness of the cook.
So don't be afraid. Go out, explore, and shoot with your favorite wide angle lenses. It maybe more useful than you think. Happy shooting!