Are there any solids with hydronium ion in its crystal structure? If so, what are they?
There are crystal structures of acid monohydrates where the acid is deprotonated and the crystal water is protonated, i.e. the hydronium salt has formed. In addition to the hydronium perchlorate (DOI: 10.1107/s0108270103010461) mentioned in ron's answer, there are structures of hydronium tosylate (Acta Cryst B 27(7), 1293-1298, (1971)) and a crown ether complexed to hydronium with perchlorate as counter ion (http://scripts.iucr.org/cgi-bin/paper?S1600536810048622) shown below.
In the animated GIF, the hydronium ions are shown as space-filling while the crown ethers and the perchlorate ions are shown as ball-and-stick. One hydrogen atoms in each hydronium ion hydrogen bonds with perchlorate. If there were a proton transfer between the hydrogen bonding partners, the structure would be perchloric acid monohydrate, but the crystal structure shows that the hydrogen atom is closer to the oxygen of the hydronium than that of the perchlorate, so calling it a hydronium salt it appropriate.
Here is another view showing the hydrogen bond (1.7 Å distance vs 1.2 Å H-O bond length), with the hydronium ions as ball-and-stick and the remainder of the structure in all-bond representation.