Original ninjhax: From 4.0.0-X up to and including 9.2.0-X, when X is between 7 and 20.
ninjhax2, tubehax: From 9.0.0-X up to and including 10.0.0-X, for X up to and including 27.
ironhax: From 9.5.0-X up to and including 10.0.0-X, for X up to and including 27.
smashbroshax with homebrew-launcher(New3DS-only): From 9.0.0-X up to and including 10.0.0-X, for X up to and including 27.
For more detailed info, see the Homebrew Exploits page.
Full system control exploits are only public for system versions up to and including 9.2.0.