I wasn't talking about the stdlib, I was talking about crates. Rust tries to keep its stdlib small so that crates can evolve on their own (and have alternatives). I think that's a valid choice, just because needing to fetch a crate for random numbers is different doesn't necessarily mean it is bad. It also means that the versioning can be different -- the URL library can make breaking changes if it wants with a major version bump, and that's okay.
Sometimes, a breaking change in the ecosystem is marked as a minor version bump, and sometimes you need to coordinate versioning across crates. This causes breaking changes for downstream users.
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Most of the actual libs with unstable rust dependencies out there are compiler plugins. "Things depending on unstable internals" exist in many communities and Rust is no different. That doesn't necessarily mean these internals should be stabilized.
A big one is clippy, which I maintain. This lints code by hooking directly into compiler APIs, which will never be stable to the extent clippy needs them to be, since that would freeze compiler evolution. Similar tools for other languages either reimplement a mini-parser+typechecker internally, or hook directly into the compiler (gimple passes, etc). There is a solution being worked on for clippy specifically. For tooling/IDEs in general, the Rust compiler will eventually get an "oracle" API that can be queried for type information and whatnot (which probably won't have enough info for clippy to work, but will have enough for general IDE stuff)
Another big one is serde, the community serialization library. There is an official one that works pretty well, but serde is better. However, the serialization codegen is done by a plugin. It can also be done with a build script on stable, but this is a bit more unwieldy. Some libraries use the plugin instead of the build script, and often break.
There is work going on for a better procedural macro/metaprogramming interface too.
That is mostly the extent of things which depend on Rust unstable internals and are used widely. There are a few more things, but they are less used.