This has been a long-considered matter. Under common law, unwanted incidental touching - say, in the context of a public space - is not illegal per se.
In Cole v. Turner (1704) 87 ER 907, Holt CJ said that:
First, the least touching of another in anger is a battery.
Secondly, if two or more meet in a narrow passage, and without any violence or design of harm, the one touches the other gently, it will be no battery.
Thirdly, if any of them use violence against the other, to force his way in a rude in ordinate manner, it will be a battery; or any struggle about the passage to that degree as may do hurt, will be a battery...
Now, I'm not sure how far American common law has diverged from English common law in this respect; it's possible that some US court has held that even such trivial contact is battery. However, I would think it unlikely, as such contact happens in the course of everyday life - a test later applied by English courts - and to make such contact tortious would likely be extremely detrimental to the functioning of modern society.
There's some discussion in comments about whether the fact that some contact is incidental or deliberate makes a difference - I submit that it does not, on the basis that unless we are incapacitated and unable to make decisions regarding the movements of our own bodies, all actions we take are deliberate.
It is also not simply a case of implied consent because then one could just hold up a sign purporting to withdraw such consent, and then bring actions in battery against everyone who brushes past them in a crowd.
As for specific criminal statutes, I can't prove a negative, but I haven't found anything that would criminalize the incidental touching of another, even in crowded places. As in Texas law, criminal assault generally requires some element of intent to harm or provoke, or the knowledge that such actions are likely to harm/provoke.