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Obviously electrons annihilate with positrons, but can a muon annihilate with an positron, or can an anti-taon cancel with a muon? similarly for quarks of different species, e.g. u and anti-strange.

I think this is possible as long as quantum numbers like charge and spin are conserved, with the excess energy being given off in kinetic energy, but has it ever been observed?

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@dmckee Thanks, your references to "Does a particle annihilate only with its antiparticle? If yes, why?" cleared completely my confusion. Also thanks to Anna.V and Marek for their explanations. –  metzgeer Jan 19 '12 at 0:03
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There are more quantum numbers to be conserve than charge and spin. There is also lepton number and baryon number and strangeness and charmness and color for strong interactions.

A muon hitting a positron can interact exchanging a photon and keep going, or a Z and turn into a muon-netrino and an electron-antineutrino through the week interaction .

Quarks are worse because they also have color, three extra quantum numbers plus charge number (1/3 or 2/3) plus baryon number(1/3).

Take the pion: pi+ is a linear combination of up anti-down and will eventually turn into a (muon+ anti-muneutrino) via the weak decay as the strong one has to conserve color.

You may call it annihilation, as you may call all interactions where the incoming particles and the outgoing differ. The customary use of the term is for particle antiparticle annihilation.

It is more complicated than you think.

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"A muon hitting a positron can interact exchanging … a Z and turn into a muon-netrino and an electron-antineutrino" - and what about $\mu^-$ $\pi^+$ interaction? –  voix Jan 19 '12 at 20:20
    
it will have to conserve muon lepton number and could go to mu neutrino plus two photons, among other things. It is not called annihilation as not all quantum numbers are annihilated. It is not an experiment that can be carried out since both the muon and/or the pion would decay before encountering each other. –  anna v Jan 20 '12 at 5:48
    
I've asked explanation of this reaction in terms of gauge bozons. –  voix Jan 20 '12 at 15:18
    
a W- will be exchanged with the quarks making up the pion. see en.wikipedia.org/wiki/File:PiPlus-muon-decay.png . It is not really annihilation since the muon leptonic quantum number is conserved. One speaks of annihilation when all quantum numbers add to zero. –  anna v Jan 20 '12 at 16:26
    
Maybe muon emits W-bozon and turns into muon-neutrino, pion absorbs W-bozon and turns into gamma? Then in muon-positron interaction muon emits W-bozon (not Z-bozon!) and turns into muon-neutrino, positron absorbs W-bozon and turns into electron-antineutrino. But what about gamma in the last case? –  voix Jan 20 '12 at 17:59
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A few theoretical samples of mixed annihilation (at low energy):

$e^- \mu^+ \to \gamma \; \nu_e \bar{\nu}_\mu$

$\mu^- \tau^+ \to \pi^0 \nu_\mu \bar{\nu}_\tau$

$\mu^- \pi^+ \to \gamma \; \nu_\mu$

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