I know there are apps that let you change tracks with the volume button. But that can be awkward (e.g. if the phone's in your pocket and you're jogging or something). I was wondering though, do you guys know of like a clip/ adapter thing that that you can use to change tracks on Android phones? I had something that could do that for my Discman back in the '90s, but I cannot find any mention of it on the internet today. You connect this adapter to the Discman, and then connect your headphones to the adapter.
Yes: there are essentially three possibilities.
Wired headphones often have extra controls inline (on the cable). You have to be careful when buying these: the way the controls signal to the phone is not standardized, so which one you need depends on who manufactured your phone. It's really easy to find "iPhone-compatible" ones, but you may have to search hard to find one which claims compatibility with your manufacturer. In that respect, things have not improved much since the Walkman days.
Bluetooth headphones can make this much easier. In Bluetooth, the media control protocol is standardized, so any Bluetooth headphones with volume and track controls will work with any phone that supports that protocol (the remote control profile). Pretty much all Android phones do, but some of the extremely low-end Chinese knock-offs might not.
Using the same Bluetooth profile, you can instead buy a dedicated remote control. This might well clip onto the cable of your wired headphones, or come in a convenient form factor (like Flow's Pebble, which is a lot more general-purpose), but it's still one extra thing to carry around.
Try Knock Control. It allows you to control music by knocking on the phone. It works even when the phone is in the pocket.