Please remember you don't have to pronounce English like a native speaker. Accents are fine! In fact, most native speakers appear to each other to have strong accents.

Pronunciation

BBC - 'Phonics tool' - this will help with SPELLING and READING - very good!
http://downloads.bbc.co.uk/skillswise/flash/phonics-tool/swf/phonics.swf
(Use Internet Explorer)

Interactive phoneme chart
http://www.teachingenglish.org.uk/article/phonemic-chart

Alphabet-Phonemes-Spellings

sounds can be spelt in several different ways, (e.g. book, should, push)
one spelling can have a different sound in different words (e.g. bear, near)

This chart shows the common spellings of the phonemes/sounds.
http://www.alphabeticcodecharts.com/One_side_ACC_with_IPA_symbols.pdf

Phonemes bookmark (printable) (with example words for each phoneme)

http://fds.oup.com/www.oup.com/pdf/elt/products/nef_int_bookmark_bw.pdf

Forvo.com
How words are pronounced differently with different accents - e.g. US / UK
Just search for a word and play the examples...
http://www.forvo.com/languages/en/

'Minimal pairs'
Practise saying difficult sounds, with lists of words which have been carefully 'paired' to contrast 2 similar sounds, e.g. /p/ and /b/
The rest of this pronunciation section is also very helpful
http://www.englishclub.com/pronunciation/minimal-pairs.htm

Pronunciation tips

BBC Learning English - choose the phoneme from the chart, listen to the pronunciation video, and see which words use the sound

http://www.bbc.co.uk/worldservice/learningenglish/grammar/pron/sounds/vowel_short_1.shtml

A tour of the British Isles in accents - regional variations

http://www.youtube.com/watch?v=-8mzWkuOxz8

Tongue twisters

http://thinks.com/words/tonguetwisters.htm#top

Learn natural English phrases - especially useful when speaking
http://www.phrasemix.com/

Mouth movements
This site shows how to make each sound, and gives videos and diagrams to help - but it's US English

http://www.uiowa.edu/~acadtech/phonetics/english/frameset.html

Listening and speaking

Dictation web site
with different levels, from gap-fills to typing everything you hear
(added to blog Feb 2014)
http://www.listen-and-write.com/

How to learn a language in 6 months - good advice!
http://www.youtube.com/watch?v=d0yGdNEWdn0&desktop_uri=%2Fwatch%3Fv%3Dd0yGdNEWdn0&app=desktop

Coursera.org For more advanced students: free, online, university-level courses from international universities! You have to sign up, but it doesn't cost anything.
I've recently been listening to 'A Brief History of Humankind'
https://www.coursera.org/

Fantastic short videos
http://www.ted.com/
Great short lectures with subtitles

English grammar videos
http://www.engvid.com/
I've not looked at many of these, but my first impression is that they are accurate, and that they will also challenge your listening skills!

Audiobooks smartphone app
There's a good free app - English Audiobooks - Librivox
The books are read by volunteers, so are of mixed quality, but my first impression was that they could be very helpful with listening skills.

How to improve your English listening
http://www.perfect-english-grammar.com/english-listening.html

Listening and vocabulary, on lots of different topics
http://esl-lab.com/
Thanks to Lian for this link

Here is a great collection of Youtube English language videos

http://www.youtube.com/user/duncaninchina/videos

Englishcentral
Lots of wonderful stuff - e.g. videos with subtitles and vocabulary help (thanks to Zhwan)
http://www.englishcentral.com/

BBC iPlayer
Re-watch programmes you have missed on television, with optional subtitles.
http://www.bbc.co.uk/iplayer/
BBC World Service
A great selection of radio programmes
http://www.bbc.co.uk/worldservice/programmes/index.shtml
The British Council
http://learnenglish.britishcouncil.org/en/how/how-greet-someone-you-havent-seen-ages
Greeting someone you've not seen for a long time: with useful worksheets.

http://learnenglish.britishcouncil.org/en/magazine
Magazine: mixed topics of general interest. Look round the website for lots more useful listening and watching activities.
http://learnenglish.britishcouncil.org/en/mobile-learning
Several apps, including word lists, a phonemes app, and podcasts.

EnglishClub

http://www.englishclub.com/english-for-work/airline-announcements.htm -
Short audio files of typical air/rail announcement.

http://edition.englishclub.com/category/listening-news/
Short news files.