While slingshots are a relatively modern invention, slings are not. They've been used as weapons, quite effectively, all over the world for thousands of years. Even King Tut had slings buried with him in his tomb.

Now I won't argue that slingshots aren't great, as they are. However, they're not something that can be easily made with items typically found in nature. That means, you have to plan to have one on you when you need it and hope it doesn't fail on you. Personally, if I'm going to the trouble of carrying a weapon with me, I'm going to carry something that packs a bit more punch anyway (like a rifle, handgun, modern bow, ect).

Now a true sling (shepherd's sling) is something that could definitely be made with items found in nature and aren't horribly complicated. Besides the sling, you've got other primitive weapons like the throwing stick, atlatl/dart, or simple bow/arrow.

With that in mind, if you've never used a sling (or atlatl), try making one and giving it a whirl (though, do be careful). It's a fun way to learn a great lost skill that heavily contributed to the survival of our ancestors. As an added benefit, you never know when it might come in handy for your survival.