For years I wondered what that weed was that always grew even if none of the flower seeds germinated.  I remember having pots full of this “weed” and it grows everywhere we water.

Here's an interesting article on Purslane:

Purslane: Not a Weed, but a Wonder Plant

Facts and Recipes on Purslane
purslaneCondemned by some as an “unsightly, pervasive weed,” purslane is also a free backyard source of protein, vitamin E, vitamin C, and the best source of Omega 3 fatty acids of any leafy plant. There’s no reason to spend money on fish oil supplements if you have this tasty food source growing in your backyard or vegetable garden.
Whether you eat it raw in salads, stir-fried, or added to soups and sauces, purslane is a delicious addition to many recipes. It’s easy to grow, tastes great, and – best of all to anyone struggling with rising food prices – it’s free.
Purslane used to be cultivated as a food crop in the United States, and is still a major food drop in many countries, including India. Its popularity has increased recently, with articles in the Washington Post and other publications highlighting the nutritional benefits and taste of this hardy little weed:

The plant is rich in vitamin E, vitamin C and beta carotene, and quite high in protein. Most noteworthy of all, it is considered a better source of essential omega-3 fatty acids than any other leafy plant. These are compounds the body cannot make itself, which are needed to complement the omega-6 fatty acids we get from grains and grain-fed meat. Wild-caught salmon and freshly hulled walnuts also deliver this prize, but for a steady supply what could be handier than a plant that leaps into your own personal food system with the ardor of an overactive puppy?

How to harvest Purslane
Harvesting purslane is easy; it grows just about anywhere that gets two frost-free months per year and loves to spread around cultivated fields, back yards, and any place that has fertile, moist soil. Even so, purslane is drought-tolerant and readily reseeds from one year to the next.
Take care when picking wild purslane though. Be sure the field hasn’t been sprayed with pesticides or other dangerous chemicals. Avoid picking directly next to roads because car exhaust can contaminate plants with chemicals and heavy metals.