Can't believe no one's mentioned E Pellicci!
'Tis on Bethnal Green Road, just east of the junction with Vallance Road. It's run by an old Italian cockney family, and opened in about 1900, and the current capo di tutti capi (good call
) is a 60-something bloke with a fine perm and a pencil moustache - he would have looked well dapper back in the day. The place is only about 20ft by 20ft square and you'll get crammed onto tables any which way, the walls are art deco wood-panelled and covered in photos of the Pelliccis with Babs Windsor, Patsy Palmer and other such east end slebs, and the food is good traditional home-cooked fare with a slightly Italian flavour. Atmosphere is fantastic, and they even have a bizarre aquarium with a vomiting Romanesque fountain in it.
Big up the Brick Lane Bagel Bake, and mention the fantastic apple strudels which are about 25p each. Also one of the few places in London you can get decent black bread. Evering bakery next door is, for the most part, not as good, but if there's a bit of a queue at the Bagel Bake their cream cheese and salad bagels are nicer to be honest.
Cafe 1001 is good, and despite its potential wankiness it just has a good atmosphere. And they do good pasteis de natas, which is pretty damn important I reckon.
Don't know much outside east London. There used to be a couple of wonderful places in Soho (some vegetarian restaurant right next to Liberty's springs to mind) but I think they're mostly closed down now.
edited to shrink Pellicci's