Varints: https://crates.io/crates/varint
Bloom filters: https://crates.io/crates/bloom
Iron: https://github.com/iron/iron
All the accessories for Iron: authentication middleware, integration with OAuth2, cookie-signing, integration with templating systems, etc. Also, an omakase framework (like Django or Rails) that pulls together a bunch of useful libraries into one crate that you can just use (with good docs) and not have to wire everything up.
Websockets: https://github.com/cyderize/rust-websocket or https://github.com/housleyjk/ws-rs
Server-sent events. I don't see a good alternative for these yet.
ElasticSearch: https://github.com/benashford/rs-es or https://github.com/erickt/rust-elasticsearch or https://github.com/KodrAus/elasticsearch-rs
An easy documentation/website generator for small libraries, that pulls examples, tests, and README files out of GitHub, runs RustDoc, and generates a professional-looking website that provides all the info that you need to get started with a library, with a minimum of extra effort for the library author. Basically, automate the job of going through libraries built to scratch someone's personal itch and "productizing" them.
Any of these could be a good project for a beginner, since there's already a lot of existing code to learn from, a small well-defined task, and an existing maintainer who has an incentive to help. Basically, just take a library, try to use it in a small test program (Linus's Law: "Never try to make a big important program. Always start with a small trivial program, and work on improving it"), and if anything is difficult or doesn't work right, figure out how to make it less difficult for the next person who runs across it and submit a pull request with that. As an added bonus, you can learn a lot of domain knowledge or basic CS data structures through digging through this, and that transfers to programming outside of Rust.
Try solving the problems without looking at the solutions first: https://github.com/brianquinlan/learn-rust
Here is a rough rank of difficultly: https://github.com/brianquinlan/learn-rust#understandability