For analyzing large chunks of data, don't use the API. Use [the *Stack Exchange Data Explorer* (SEDE)][1], that's what it's there for.  SEDE data lags real-time by 1 to 5 weeks, but that's no big problem for most statistical purposes.

For intense "Big data" analysis beyond even SEDE's capabilities, use [the quarterly data dumps][2]. (Thanks, Tim Stone, for the reminder.)

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If you really must use the API, follow these guidelines:

 1. [Register your app][3].
 2. Make sure you do not bust your [quotas][4].
 3. Monitor and respect [the `backoff` flag][5].
 4. For anything more, contact the API team and negotiate for special access.


  [1]: http://data.stackexchange.com/help
  [2]: https://archive.org/details/stackexchange
  [3]: http://stackapps.com/apps/oauth/register
  [4]: https://api.stackexchange.com/docs/throttle
  [5]: https://api.stackexchange.com/docs/wrapper