Is there any way to annihilate matter without the use of anti-matter? Is there any way to annihilate matter without the use of anti-matter? And vice versa? I mean, for example is it possible to totally convert the mass of a proton into "pure energy" without use an anti-proton?
 A: I just started here so I don't have the rep. to comment and I don't have the time for a full answer, but the black hole idea mentioned in the comments above is a fine answer.  See, for example, http://arxiv.org/abs/0908.1803v1 and How would a black hole power plant work?
A: A proton has a positive charge so by charge conservation it is not possible to reduce a proton to uncharged radiation particles such as photons (assuming that is what you mean by "pure-energy") Because of gauge invariance charge conservation is likely to hold good in all future physics, but we can't be totally sure of that.
It is possible that some charged massless particle will be discovered but that seems unlikely. If such a particle existed a proton might decay to that and you might consider that as "pure-energy".
If we ignore the "example" of a proton and consider the original question, the answer is that it may be possible to reduce an atom to photons but this is very difficult since it violates baryon number conservation. This has never been observed but there is theory that tells us that baryon number non-conservation is possible in the standard model using non-perturbative effects. It may also be possible to violate baryon number using beyond standard model physics or by throwing matter into a blackhole and recovering Hawking radiation. It is not possible to violate charge conservation this way (according to our best theories) but it should be possible to violate baryon number conservation (unless there is a hidden unknown reason why it is not possible) The same applies to lepton number for electrons.
So according to our current state of knowledge reducing an uncharged atom to photons is probably possible in principle but we have no experimental evidence to support this claim and it is unlikely to be something we can ever do in practice due to the low rate of baryon and lepton number violations in all known theories. 
Some theories about the final state of the universe (such as Penrose's conformal cosmology) assume that on very very long timescales all matter will be reduced to photons in this way and these will lose their energy as the universe expands so that only dark energy (balanced by an opposing quantity of negative gravitational energy) remains. 
A: The definition of an antiparticle is dependent on having the opposite  quantum numbers of the particle so that they can annihilate, i.e. the sum of the conserved quantum numbers are zero. Thus the answer by @mpv is adequate.
The implication of your question is then: is baryon number conservation a strict law or an emergent law that may be violated at some small probability.
There exist models where protons can decay with very long lifetime, dependent on the model. for example,   of a model
$$\mathrm p^+    \to    \mathrm e^+    +    π_0
\quad\text{and then}\quad π_0    →    2γ.$$

so one would get two photons and an electron from this decay.
Now from the Feynman graph it is evident that it is a quark that disappears . The question though involves a proton disappearing. One can see from the diagram reading it from top down, right to left that if one scatters an $\mathrm e^-$ on a proton there exists a probability that the proton will disappear and a $\pi_0$ will manifest and decay into two photons.( a third particle should be involved  in order to get a $\pi_0$ due to momentum conservation otherwise one would get two quark jets, maybe a second $\pi_0$) 
So this is may be an annihilation of a proton into photons with the appearance of two pions minimum. It does conserve charge ( or B-L quantum numbers). 
The limits of proton decay are pushed further and further with each experiment and thus this inverse reaction will have such a tiny probability that one cannot perform it in the lab and wait for results. 
A: I am assuming that by "energy" you mean photons. So you want to transform protons into photons.
It is not possible. It would violate several conservation laws - mainly the charge conservation (protons are positively charged), but also baryon number conservation.
The antiparticle is necessary to cancel these quantum charges to make the transition possible.
A: The simple answer to the main question is, yes.  There are two ways to annihilate matter without using anti-matter.  One is called fission, and the other is called fusion.  Although only some of the matter is converted into energy in either of these processes, the efficiency of the "annihilation" is not in the main question. If 100% annihilation is required, then only anti-matter will do it.   
A: Note that this is possible even if we restrict ourselves to stay within the rigorous realms of the Standard Model. E.g. the deuteron is known to be unstable, it will decay via instanton tunneling to a positron and an anti-muon neutrino (or an anti-muon and anti-electron neutrino). The deuteron lifetime would be about 10^(218) years if this Standard Model process were the only process contributing to its decay.
