The term "[well tempered][1]" is generally used for what you refer to in the end: a temperament that is not-equal, but is (reasonably) playable in any key.  The [Werkmeister tunings][2] are the most well known of this sort.  It's my impression that many pipe organs are still tuned in this manner (so that is the context you'll often hear it in), due to way that the sustained nature of the notes works with the common repertoire. 

(Disclaimer I'm not a violinist)
In terms of violin performance I've heard the following: if you tune your violin using harmonics just by ear so that they form perfect (consonant) fifths, so that G->D is a perfect 5th, D->A is a perfect fifth and so on.  The interval between the G and E string is a [Pythagorean sixth][3], which is noticeably off (to some people) from a (5-limit) just intonated 6th and/or an equal tempered major 6th.  So some violinists "temper their fifths" when tuning by ear, though by [no means is this universally accepted][4] as ideal, [especially not in all situations][5], e.g. [playing with a fixed pitch instrument][6].


  [1]: https://en.wikipedia.org/wiki/Well_temperament
  [2]: https://en.wikipedia.org/wiki/Werckmeister_temperament
  [3]: https://en.wikipedia.org/wiki/Pythagorean_interval
  [4]: http://www.violinist.com/discussion/response.cfm?ID=18867
  [5]: http://music.stackexchange.com/a/17772/2639
  [6]: http://music.stackexchange.com/a/17759/2639