Here is a weed that I ate today that has a great non-bitter flavor. Many describe it as being "spinach-like". A girl that I was with told me of all of it's medicinal uses and that her friend loves this weed so much...that she got a tattoo of it! While I wouldn't recommend having this weed indelibly inked on your body...I do think it is a good one to learn to identify....for food and medicine. Take note that there are some precautions regarding eating it.
Here is a video by Green Deane where he gives some great info on how to identify it. His video has a pretty sparse looking chickweed. The Chickweed I ate locally looks more like the picture to the right.
Here is a video that has a more luscious looking chickweed and mentions it's use as a diaper rash remedy.