I've only read an excerpt of Sara Stein's book, My Weeds (in the highly-recommended compilation The Writer in The Garden, shown in my book list in the right-hand column), but it's one I'm searching for in my second-hand shopping expeditions.
My own list of weeds includes this year's worst offender, purslane (Portulaca oleracea) shown above. I'm forever reading about how this weed is edible and incredibly nutritious. I've even seen it for sale at the farmer's market. We've eaten it raw and briefly sauteéd, but I could never eat all that comes up in our small yard.
I sort of mentally rate various weeds by how difficult they are to pull and tend to feel less hatred for the easy ones. Moderately easy-pulling hairy galinsoga (Galinsoga ciliata) is an exception to that tendency because it grows so vigorously and profusely in warm weather. I yanked this one from the ground and left it on the pavement to die, but a light rain revived it and its stems craned up toward the light. It is also supposedly edible, but tastes bad to me.
Prostrate Spurge (Euphorbia maculata) almost looks pretty to me, but having allowed it in one corner long ago, I learned my lesson. It has a taproot which makes it difficult to pull out and thrives in sidewalk cracks.
Common Fleabane (Erigeron philadelphicus) is another common sight which has small daisy-like flowers (don't be tempted) that spread like wildfire, but are easy to pull.
Everyone has seen Oxalis, which looks like clover. This stuff is also taprooted and hard to remove effectively. I try and pull this when its tiny.
I must look up the name of this familiar, low growing, easy to pull weed. A great reference book we have at work is Weeds of the Northeast, by Richard H. Uva; Joseph C. Neal; Joseph M. DiTomaso. It features 3 photos of each plant, close-up and from a distance and as a seedling.
I could go on and on with this list. These are just a few I photographed yesterday morning.
Update: My co-worker Charles Day informed me that this is the aptly named Carpetweed, (Mollugo
verticillata) and a member of the Aizoaceae family.