There is what is known as "Galactic Cosmic Radiation", which is much the same as the solar wind (high energy atoms, ions and electrons) from our own sun, but comes from all other sources in the galaxy, and perhaps other galaxies.
See -
http://www.sievert-system.org/WebMasters/en/contenu_rayonnement.html[/URL]
[PLAIN]http://rise.hao.ucar.edu/iscs/abstracts/node99.html[/URL]
[url]http://hesperia.gsfc.nasa.gov/sspvse/oral/Ken_McCracken/wintergreen1.pdf[/url] (use save target as)
[PLAIN]http://aoss.engin.umich.edu/Radiation/presentations/Shea-Smart.pdf[/URL]
http://www.nature.com/nature/journal/v255/n5511/abs/255687a0.html;jsessionid=D3C86159CC3D1A72216F9744FB4527D1
There exists an spectrum of energy of Galactic Cosmic Radiation, with the higher energies >> being relatively rare.
Particles with energy as high as 10[sup]20[/sup] eV have been reported, and these are certainly near the speed of light. Consider that a single nucleon (proton or neutron) has rest mass slight less than 0.940 GeV.