I seem to mostly have crumbs and sticks these days... but I guess that wasn't the question!
You sort of need everything as it's been said before and it really depends on the age, like other posters I find I have more now when DS is 2.5 than when he was a baby.
To start with you only really need the mat, nappies, nappy bag, wipes, change of clothes 1 or 2, dummies if you want, muslin plus all your stuff.
With DS I carry, 3 or 4 pairs of pants, wipes, changing mat in case of big accident, 1 pair of trousers, 1 pair of socks, 1 jumper, beaker, snacks, back up snacks and emergency bribe snacks he doesn't know about, kiddie alcohol wipes, arnica cream, plasters, suncream, sunglasses, hat, my purse, phone, lipbalm, snack and drinks for me too :o