QUARKS

In everyday life, no. Quarks are subject to color confinement. Any attempt to separate a quark from its partners will fail. You can’t pull hard enough to break a quark out of, say, a proton (3 quarks) without pulling so hard that the energy you’re using produces a new quark-antiquark pair, so you end up with the same proton and a pion (1 quark and 1 antiquark) and still no free quarks.

Here’s a nice animation by Manishearth from Wikipedia, showing what happens if you try to pull one of the the quarks out of a pion:

However, there are some exceptions.

At temperatures above around 2 trillion degrees, hadrons (particles made of quarks, like protons and pions) cannot exist. Quarks flow freely through a sea of gluons, sort of like ions flowing through a sea of electrons in a plasma (although actually it probably acts more like a superfluid than like a plasma), so this state is called quark-gluon plasma. The entire universe was this hot for the first 10 microseconds or so. Since then, we can very briefly produce a tiny bit of quark-gluon plasma in our supercolliders (and presumably so can alien physicists), and there are some extreme cosmological events that also probably briefly produce it—but that’s it.

At lower temperatures but insanely high pressures, there are different states of matter where quarks can flow freely. These conditions didn’t exist in the early universe, and we haven’t figured out how to produce them in a lab yet, but they may be going on deep in the core of large neutron stars.

Finally, the heaviest flavor of quarks, top quarks, are so heavy, and therefore unstable, that they decay faster than they can be confined. So, a top quark does sort of “exist by itself”, but only because it barely gets a chance to exist at all.

But we don’t live at temperatures over 2 trillion degrees, or at neutron star core densities, and we’re made of up and down quarks (with maybe the occasional strange), not top quarks. So, all the stuff you see going on around you, there are no free quarks anywhere. Everything is hadrons, quarks stuck together and confined.