If you refer to electromagnetic radiation, the answer is: the major part of radio, all microwaves, and also infrared of low frequency, and also obviously, the visible range. IR of high frequency and higher frequencies than the visible are all blocked by the atmosphere, as well as radio of very low frequency. The fact that some radio waves can reach the surface is useful, so we can have monstruous radiotelescopes like that existing in Arecibo, Puerto Rico
Neutrinos can pass freely through the atmosphere, as they practically don't interact with matter.
There are also cosmic rays. Primary cosmic rays habitually don't reach earth's surface (though a few achieve it); practically all secondary cosmic rays reach Earth surface (secondary cosmic rays don't come from any extraterrestial source, they are created by the collission of primary cosmic rays with the atmosphere)
The earth's atmosphere is not very astronomy friendly, albeit even astronomers prefer living on a planet that has an atmosphere. There are a number of probes and orbital 'observatories' [eg, Hubble telescope] used to scope out stuff not visible, or poorly visible from earth. There may also be other particles that we do not yet know exist because they rarely interact with ordinary matter [like neutrinos, which we knew must exist well before we actually detected them] or interact so weakly their effects are very difficult to detect [like gravity waves].
Just to add a few words on 'cosmic rays': these are comprised of particles (e.g. protons, Fe nuclei), EM (gammas), and neutrinos (tho' 'cosmic rays' doesn't usually include neutrinos). As meteor said, few, if any, particles reach the Earth's surface - they collide with nuclei of oxygen, nitrogen, etc (in the upper atmosphere) and generate 'air showers', which are cascades of secondary particles. These air showers are observable down here, under all the air, and there are a number of very powerful 'cosmic ray observatories' on (or under) the Earth's surface. However, as most cosmic ray particles are charged, they are affected by the galactic magnetic fields, so all information about their original direction is lost by the time we 'see' them (we can tell from which direction they were coming when they hit the atmosphere, but not where they started out).
The gammas, being neutral, aren't affected by magnetic fields. However, they don't reach the surface of the Earth either - they are detected by Cherenkov radiation, which arises because the speed of light in air is lower than that in vacuo. There also several such 'TeV gamma cosmic ray telescopes' (the 'TeV' refers to the energy of the gammas - the 'T' means 10^12, i.e. 1,000 billion).
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