I'm not familiar enough with the proofs to say if they are more than superficially different, but here is something:

1) [Moeglin-Waldspurger][1] prove continuation crediting Jacquet (who cites Selberg), instead of Langlands. They say it is similar to that given by [Efrat][2], in his treatment of the Hilbert-modular ($PSL_2$ over a totally real field) case.

2) [Colin de Verdière][3] gave a "new and strikingly brief and elegant proof" (from the MR review) for $SL_2({\mathbb R})$ (extended [here][4]). [Muller][5] also has a proof in the rank-one case. They both seem to be related to scattering theory (also see [Lax-Phillips][6]). It's worth noting that I can't find a treatment for general reductive groups using these methods.

3) [Wong][7] gave a proof using integral equations.

All the ideas seem to go back to Selberg.

  [1]: http://www.ams.org/mathscinet-getitem?mr=97d%3A11083
  [2]: http://www.ams.org/mathscinet-getitem?mr=88e%3A11041
  [3]: http://www.ams.org/mathscinet-getitem?mr=83a%3A10038
  [4]: http://www.ams.org/mathscinet-getitem?mr=84k%3A58222
  [5]: http://www.ams.org/mathscinet-getitem?mr=98f%3A11053
  [6]: http://www.ams.org/mathscinet-getitem?mr=58%3A27768
  [7]: http://www.ams.org/mathscinet-getitem?mr=91c%3A11031