Free and Open Source Machine Translation API, entirely self-hosted. Unlike other APIs, it doesn't rely on proprietary providers such as Google or Azure to perform translations. Instead, its translation engine is powered by the open source Argos Translate library.
Supports per-user limit quotas, e.g. you can issue API keys to users so that they can enjoy higher requests limits per minute (if you also set --req-limit). By default all users are rate-limited based on --req-limit, but passing an optional api_key parameter to the REST endpoints allows a user to enjoy higher request limits. To use API keys simply start LibreTranslate with the --api-keys option.
There are also F/OSS mobile clients for Android and browser plugins.
Free and Open Source Machine Translation API. 100% self-hosted, no limits, no ties to proprietary services. Run your own API server in just a few minutes. Playing with it a little, it seems like it might be interesting to experiment with. Supports a couple of languages right now, but at least they're useful ones.
API docs: https://libretranslate.com/docs/
Github: https://github.com/uav4geo/LibreTranslate
The back end appears to be written in Python. Examples of use are in Javascript, but that's not necessarily the way it has to be done.
Language models are kept in a different repo: https://github.com/uav4geo/LibreTranslate-Models
An AI assisted online translation service, positioned as an alternative and rival to Google Translate. Translate text online, from a desktop application, or using their API (which has a separate billing plan - $5.56 per month, plus 1 cent per 500 characters). Supports 72 possible pairs of languages, with more being added. The basic account is about $10us per month (annual subscriptions are somewhat less per month, aggregate).
A F/OSS natural language translation system that seems to want to give Google Translate a run for its money. The corpuses used for training appear to be crowdsourced, and I think you can download the trained models on their own. Aims to be self-hosted.
Github: https://github.com/apertium
Installation docs: http://wiki.apertium.org/wiki/Installation
An open source software project for converting sequenced DNA into music. Well beyond simply assigning notes to nucleotides, whose pieces can be played simply by interpreting the electrochemical properties of a DNA sequence in different ways. The site allows you to upload your own pieces as well as listen to those of others (oh, and download the software).
MyMemory is an online translation system that uses both machine implemented translation and human-contributed translations, probably with some form of machine learning on the back-end. Users can upload files with their own translations to improve the service's accuracy. These documents, called memories, can either be public or private. They are also working to make translations more readily searchable. They have a REST API that we can use.