You Can use Twitter Search API and Streaming API to retrieve recent and Real time Tweets from Twitter. Although, The number of Tweets is limited, but they are very efficient for Twitter data.
This very much depends on the privacy / data sharing rules and the volume of the particular social network you want to use (also on your ability / willingness to write codes).
scraperwiki.com is a great website to get basic data from Twitter.
NodeXL is a nice software to both extract data from Twitter (as well as from Facebook) and analyze social networks.
R's TwitteR package is also pretty decent - http://cran.r-project.org/web/packages/twitteR/index.html
If the social network does not have an API that you can use to retrieve data from, you can always go 'old school'. I have a colleague who practically went through the forums and copied/pasted comments to a Word file.
Social Media Analytics allow you to search by time and place, alerts set, and analyze sentiment for every tweet ever made: http://topsy.com
To measure the number of impressions and reach of hashtags: https://tweetreach.com
Search engine within Twitter. Through keyword-based and / or location searches this tool shows you the accounts that meet these criteria so that you can filter by number of followers, number of tweets and accounts (VERY GOOD): http://followerwonk.com/
To measure the influence of a twitter account: www.kred.com
Twitter mentions Displayed in a map: http://mentionmapp.com/
Infuence of hashtags: http://hashtagify.me
To searc hwithin Twitter: Twitter.com / search-advanced
Social intelligence research tool: http://es.twtrland.com/
Twitter provides access to its Search API that can help you extract data for any hashtag, keyword, phrase, or account. However, for an end-user, it might be tricky to set up the API without a fair bit of coding expertise.
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As someone that has and still is performing market research, I understand that getting raw data is tough. Right now I'm combining my research about Millennials and Sustainable consumption with a full-time job at a company called Tweet Binder (tweetbinder.com), which is specialised in Twitter analysis.
We've full access to Twitter's data and our tool lets the user analyze hashtags, keywords, accounts... back in time as well as in real-time. We've got a very cool visualization panel with which you can classify all the tweets of a report in binders as you please: originals, with images, with links, conversations...
We provide all Twitter's metrics as well as our unique Economic Value and Sentiment Score statistics, as well as downloadable Excel, PDF and JSON files.
If you want you can DM me here in Research Gate or send a non-binding e-mail to [email protected], I'll be happy to share an example with you.