Implementations of BSON exist for many different programming languages. Some implementations are currently embedded within MongoDB drivers, since MongoDB was the first large project to make use of BSON. Over time those libraries will be made more stand-alone, but they should be usable independently of MongoDB in their current state.
Most of these libraries use the Apache 2 license, but check individual project details to confirm.
libbson - A library providing useful routines related to building, parsing, and iterating BSON documents. Used by the cross-platform libmongoc client library that provides a base for MongoDB drivers in higher-level languages.
C# / .NET
The MongoDB C++ Driver Library - The official MongoDB C++ driver includes a robust and well tested BSON implementation. You can use just the BSON portion of the driver library if desired.
github.com/jbenet/bson-cpp - A standalone C++ BSON implementation forked from the MongoDB C++ driver, with the non-BSON code pruned away.
github.com/dwight/bson-cxx - Yet another C++ BSON implementation originating from the MongoDB C++ driver. Non-BSON code was eliminated, Endian-awareness was added, and some attempts were made to simplify the interface.
JSON for Modern C++ - A library to make JSON a first-class data type in C++ which can read and write a subset of BSON that can map to JSON.
jsoncons - A C++ header-only library for constructing JSON and JSON-like data formats including BSON, supports encode/decode of BSON byte string.
vibe.data.bson - BSON serialization and value handling.
bson_codec - A flexible serializer and deserializer for BSON documents.
The BSON library (org.mongodb.bson) - A standalone BSON library, with a new Codec infrastructure that you can use to build high-performance encoders and decoders without requiring an intermediate Map instance.
bson4jackson - A pluggable BSON generator and parser for Jackson JSON processor.
ebson - Extensible BSON encoder/decoder library written in Java with pluggable Java-to-BSON type mappings.
Jongo (org.jongo.bson) - Included in the Jongo driver for MongoDB.
CookJson - Contains JSON and BSON parsers/generators for JSON API for Java (JSR 353).
BSON.jl - A Julia package for working with the Binary JSON serialisation format.
cl-mongo - Common Lisp interface for MongoDB.
bson - BSON serialization and deserialization library used by the official MongoDB Node.js driver.
Bson.ml - A BSON encoder / decoder in OCaml, built for MongoDB.
BSON - Interface included with the official MongoDB PHP driver. Builds on the libbson C library.
prolog-bson - BSON encoder/decoder for Prolog. Used by the Prolog MongoDB community driver prolongo.
bson - Encoding and decoding support for BSON built using the Serde framework.
Mongo-BSON - Part of the MongoTalk driver for MongoDB.
mlmongo - Standard ML driver for MongoDB.
MongoDB - A distributed document-oriented database using BSON as both the network and on-disk representation of documents.
ModeShape - A hierarchical JCR data store using BSON to serialize the data.
bsonsearch - BSON matching engine to perform offline document comparisons without a MongoDB server. C dynamic library with Python wrapper.
If you know of other BSON implementations or projects using BSON, please add them.