Could we make things out of newly discovered particles? Right now, all of the "stuff" that has been created in the world is made of protons, electrons, and neutrons. I'm aware that particles other than these have much shorter lifetimes. But I've also heard that mixing particles in the same state can increase their lifetimes - the neutron, for example, has a half life of 15 minutes when it's alone, but is stable in an atom.
Could we make combinations of other particles that last for (at least) days at a time? The combination need not consist entirely of new* particles, it must just have at least one.
I am very interested in this subject, so ideally I'd like a concrete answer, not just a guess.
 A: I am not a physicist, so I am at large risk of answering wrong things, but I am surprised no one has mentioned antimatter yet. Anti-hydrogen atoms, says Wikipedia, have been observed for as long as 1000 seconds, and as far as I know there are no physical obstructions to them surviving for almost* infinitely long (as long as there is no ordinary matter around).
*I put an "almost" here because of proton decay.
A: This is really just an extended comment on CuriousOne's answer.
You probably know that there are just a few elementary particles: six quarks, three electron-a-likes (electron, mu and tau), three neutrinos and various assorted bosons. All matter is made up from various combinations of these particles.
The problem is that the heavy particles decay into the light ones on short timescales. So top, bottom, charm and strange quarks end up as up and/or down quarks while tau and mu end up as electrons. So very quickly everything ends up as electrons and up and down quarks, which of course make protons and neutrons.
The energy difference between up and down quarks is relatively small, and indeed it's comparable to nuclear binding energies. That's why a neutron can be stable in a nucleus and unstable out of it, because the nuclear binding energy is large enough to stabilise the neutron. However in all other cases the energy difference between the different types of quarks is far larger than nuclear energies and (apart from some special cases - see below) there is no stabilising them. Likewise the energy differences between the electron, mu and tau are too large for the heavier particles to be stabilised by atomic binding energies.
I've skipped over the bosons because you can't make matter from bosons. Bosons don't obey the Pauli exclusion principle, and it's the exclusion principle that allows atoms to exist. If you attempted to make matter from bosons at best you just get a condensate.
I did say there we some special cases. Let me start with a known one: you can make matter from muons. Muonic hydrogen has been made, and so has a hydrogen analogue made from an anti-mu and electron. I thought the mu/anti-mu equivalent of hydrogen had been observed, but Wikipedia says not. Anyhow, these atoms last only until the mu decays. As mentioned above, the binding energies available are too small to stabilise the mu and prevent it decaying to an electron.
The other special case is still entirely theoretical. A neutron is stable because the nuclear binding energy is high enough to prevent the down quark to up quark decay, but nuclear energies aren't high enough to prevent for example a strange quark decaying. However it has been suggested that at exceedingly high pressures the strange quarks could be stabilised and form strange matter. Most of us regard these ideas as huge fun but rather unlikely.
A: Well, the "new" baryons are really just expected short lived combinations of quarks. The only stable free ground state of quarks are protons. The free neutron has already a slightly higher energy than the proton, which makes it unstable. Only the interaction with other protons and neutrons inside of nuclei can stabilize this quasi-stable particle. Given their mass of six times proton mass there is no reason to believe that there can be any form of stabilization for these newly discovered baryons. So the answer is "No". Neutrons were discovered in 1932, not so recently.
Having said that, the question is a good one, if we generalize it to "Can there be more stable elementary particles?". The answer to that is "Yes". Dark matter searches, for instance, are focused on just that kind of object. In case of cold dark matter, of course, the chances of finding "lumps" of it are marginal. If anything those particles seem to interact in almost no other way than by gravity. 
On a technical level this opens up into the question whether the standard model is supersymmetric, with a second set of superpartners existing at some higher energy range. The question is open, even though the current status of LHC data does not look good for supersymmetry, if I understand the interpretation correctly. I will let a theorist give a real answer to that. 
A: As far as I know, there are some neat plans with anti-matter. It is higly theretical, but somehow it could be possible to create "new" elements by bounding anti electrons with electrons in strong magntic field. The aim of this idea is to store anti matter in "stable" state so it wouldnt anihilate with matter (usually very vigorous action - creating gamma rays).
