Another common one:
Its or It's
As far as text messaging via chat... it just makes it easier and I don't consider that a grammatical fallacy.
ns, gs, n1, vns, gr8 shot, nt, np, gp, vnp, nr, nd, ul, bs, n up, n out, n save, and of course (my personal favorite) #%#!%^!!.
I'm sure I missed a few....