Grows like a weed (and is one in many vegetable gardens); the leaves, however, are very healthy and appear in salads, or cooked with chives or garlic. Lately it is becoming a little popular again, and Italians are putting it in piadine, malfatti and other recipes. Purslane is loaded with omega-3's and other good things, and it has always had many medicinal uses.
Many dialect names, especially in the south: barzellana, perchiacca, perchiazza, porcacchia, portulaca, precacchia, pucacchia, purciaca, purchiddana, etc. In Lombardy it's erba grassa.
Don't ask them for porcellana fredda though. That's a kind of modelling paste made from corn starch for hobbyists.