Wikipedia list of Quantum Computer programming languages
(This answer is not a copy of that webpage, it's more updated and with verified links. In some cases the author's paper or website link is added.)
The website Quantum Computing Report has a Tools webpage listing over a dozen links, some new and some repeating the above list.
Are there certain benefits to choosing particular ones?
If you plan on using a particular quantum computer then one would hope that the programming language developed by the manufacturer is both best suited for that particular machine and well supported.
Choosing a language with a larger following means that there are more Forums available and hopefully more bug fixes and support.
Unfortunately, that leaves some great niche products to struggle to gain a user base. Trying to find one language that is both powerful/expressive and supported across various platforms is the trick, the answer is an opinion ATM.
An evaluation of four software platforms: Forest (pyQuil), QISKit, ProjectQ, and the Quantum Developer Kit is offered by Ryan LaRose in "Overview and Comparison of Gate Level Quantum Software Platforms" (6 Jul 2018).
Google's Cirq and OpenFermion-Cirq: "Google's AI Blog - Announcing Cirq: An Open Source Framework for NISQ Algorithms".
D-Wave's Leap and Ocean SDK allows access to a D-Wave 2000Q™ System in a cloud environment with access to a 2000+ qubit quantum annealing machine to test and run workloads for free, assuming the core algorithms used go into the open source pool. Apply to login at D-Wave's Leap In webpage.
Rigetti Computing's Quantum Cloud Service (QCS) offers a Quantum Machine Image, a virtualized programming, and execution environment that is pre-configured with Forest 2.0, to access up to 16 qubits of a 128 qubit computer.
Stay tuned for information on Fujitsu's Digital Annealer, an architecture capable of performing computations some 10,000 times faster than a conventional computer. If they eventually provide a development environment that is cross-compatible with true quantum computers these two paragraphs will remain in this answer, otherwise I will remove them.
While their silicon chip is not quantum in nature Fujitsu has partnered with 1Qbit to develop what is described as a "Quantum Inspired AI Cloud Service", whether their Digital Annealer quacks like a duck (anneals like a D-Wave, and uses compatible code) remains to be seen. Visit here to access the Fujitsu Digital Annealer Technical Service.
University of Pennsylvania's QWIRE (choir) is a quantum circuit language and formal verification tool, it has a GitHub webpage.
A review of: Cirq, Cliffords.jl, dimod, dwave-system, FermiLib, Forest (pyQuil & Grove), OpenFermion, ProjectQ, PyZX, QGL.jl, Qbsolv, Qiskit Terra and Aqua, Qiskit Tutorials, and Qiskit.js, Qrack, Quantum Fog, Quantum++, Qubiter, Quirk, reference-qvm, ScaffCC, Strawberry Fields, XACC, and finally XACC VQE is offered in the paper: "Open source software in quantum computing" (Dec 21 2018), by Mark Fingerhuth, Tomáš Babej, and Peter Wittek.
I will return to this answer from time to time to make updates, without excessive bumping.