Character sheet, dice, a writing implement, and other -- namely, whatever else they need to play their character.
If everything they need to reference is in their character sheet, it doesn't matter if they have a PHB or not; but if they are playing a spellcaster, and will need to look up spells, bring the books with the spells. Someone else is usually the host, not me, and if I GM, I may bring no D&D books -- no PHB, since I have an SRD, and I bought the Spell & Magic Item Compendiums, and my favorite monster books, in PDF, and I'm not loaning anyone my laptop.
They might want to bring notes, 'cause I'm not always going to remember to remind people of basic campaign facts & the like, so if they forget who the villain is and get suckered because of it . . .
Of course, my D&D game is over, so I guess the real answer should be "nothing".
