Presidential candidates, 2016 - Ballotpedia has a timeline of announcements of who's in and who's out.
Republican:
Ted Cruz: 2015 Mar 23 -
Rand Paul: 2015 Apr 7 -
Marco Rubio: 2015 Apr 13 -
Ben Carson: 2015 May 3 -
Carly Fiorina: 2015 May 4 -
Mike Huckabee: 2015 May 5 -
Rick Santorum: 2015 May 27 -
George Pataki: 2015 May 28 - 2015 Dec 29
Lindsey Graham: 2015 Jun 1 - 2015 Dec 21
Rick Perry: 2015 Jun 4 - 2015 Sep 11
Jeb Bush: 2015 Jun 15 -
Donald Trump: 2015 Jun 16 -
Bobby Jindal: 2015 Jun 24 - 2015 Nov 17
Chris Christie: 2015 Jun 30 -
Scott Walker: 2015 Jul 13 - 2015 Sep 21
John Kasich: 2015 Jul 21 -
Jim Gilmore: 2015 Jul 29 -
Democratic:
Hillary Clinton: 2015 Apr 12 -
Bernie Sanders: 2015 Apr 30 -
Martin O'Malley: 2015 May 30 -
Lincoln Chafee: 2015 June 3 - 2015 Oct 23
Jim Webb: 2015 Jul 2 - 2015 Oct 2
Lawrence Lessig: 2015 Sep 6 - 2015 Nov 8
Green:
Jill Stein: 22 June 2015 -
Ben Carson's staff seems to be fleeing his campaign and joining the likes of Ted Cruz.
From Ed Brayton of Dispatches from the Culture Wars:
Carson Loses Most of His Senior Campaign Staff -- his national staff
Carson Loses More Staff, This Time to Cruz -- his New Hampshire staff