General

• Google APIs & Developer Products
• Google Fusion Tables
• data.nasa.gov  (includes API)
• Programmable Web has a great directory of web mashups as well as a list of APIs that can be used to builds them and a HowTo Tutorial page. 

Social Networks

• Facebook - API reference, Tutorial using PHP
• LinkedIn - API reference, Tutorial on using OAuth with LinkedIN

Media 

• Spotify
• Netflix
• Last.fm ans an API which gives you information on what music members are listening to and have been listening to etc.  

Maps

• Google Moon and Google Mars
• NASA Extenstions to the Google Maps API
• OnEarth from NASA's Jet Propulsion Laboratory
• Open Street Maps Data 

Museums

• Cosmic Collections API from The Science Museum 

Astronomy

• Astronomy LookUP from Jodrell Bank 
• flickr.photos.astro — YQL open table returning feeds of coordinates and names for tagged astronomy photos.
• starchartjs — Not an API as such. Javascript library for drawing starcharts in <canvas>. Includes bright star catalogue, constellation figures and ephemerides for the planets.
• starchartjs (SVG) — Javascript library for drawing star charts with Raphaël. Possibly better cross-browser compatibility than the <canvas> version, but slower. Includes bright star catalogue and constellation figures.
• Sloan Digital Sky Survey (SDSS) SkyServer — access spectra and images from the survey.
• CDS XML Web Services — convert astronomical coordinates via API.
• SETI Institute Data - they've just announced upcoming APIs for some of their data.
• NASA Extensions for Google Maps - mostly maps of the Moon and Mars
• WFCAM - access to the UK Infrared Deep Sky Survey (UKIDSS)
• Digitized Sky Survey - access the DSS by position on the sky.
• SkyMorph/NEAT - Repository of Near Earth Asteroid Tracking CCD images
• WorldWide Telescope Script Reference — Javascript API for embedding Microsoft WorldWide Telescope in web pages. Allows you to programme tours of the sky, embed external images, view other planets. 
• Zooniverse APIs - We are creating APIs in time for this event, such as Galaxy Zoo and Moon Zoo live classification feeds (see http://www.moonzoo.org/live). Feedback/suggestions welcome email robert.simpson@astro.ox.ac.uk.
• ...

Photos

• Flickr
• Astrotagged photographs
• Searching astro:name with YQL (Has some javascript for placing flickr photos in the sky)
• Generating astrotags from astrometry.net photo comments 

Messaging

• Twitter
• Tropo - SMS, IM and voice communications API, free for development

Location

• Geoloqi - Send users notifications when they enter a certain area
• Instamapper - Free Real-Time GPS Tracking 

Data Logging

• Pachube

   

Genetics

• Ensembl has a public MySQL server, a datamart and an API which you can use to query genomes and annotations.
• JBrowse - portable JavaScript genome browser

Biodiversity

• Global Biodiversity Information Facility: species occurrence records, as well as classifications and scientific and common names

Molecular Biology

• EBI: nucleic acid, protein sequence, and macromolecular structure data

Literature Annotation and Recommendation

• Journal Author Name Estimator undocumented api, for an example implementation look at (http://github.com/IanMulvany/janey-robot)
• http://reflect.ws/ http://reflect.cbs.dtu.dk/restAPI.html returns annotations on documents with info on identified gene and proteins.  
• Biodiversity Heritage Library 

Climate & Environment

• AMEE: environmental impact calculation API (Use AMEEdiscover to find things)
• Climate data api: From the  World Bank.  Also there's a competition to create apps for climate (deadline 16th March)

News and commentary

• Guardian Open Platform (API Explorer)

Publications

• Pubmed/EUtils API
• CrossRef search (most scientific research has a unique identifier, a DOI, CrossRef maintains the index)
• The Physics ArXiv  http://arxiv.org/help/api/index
• Eprints archive  http://wiki.eprints.org/w/Category:API 
• Scopus APIs 
• Mendeley 
• FigShare 
• PLoS Search API
• PLoS ALM (alt-metrics) API
• William Gunn's list of APIs, datasets, and tools. 
•  Nature.com Blogs API   
• Connotea API (delicious for papers)  http://www.connotea.org/wiki/WebAPI 
• Bibsonomy API http://www.bibsonomy.org/help/doc/api.html 

Other collections

• London Green Hackaton
• Cleanweb