I recently discovered their similarity when I mistakenly identified a patch of weeds on my husband's family farm as Queen Anne's Lace to my children. I looked closer, however, and realized that the flower umbrells were too curved, and there were too many of them. My curiosity led me to ask my brother-in-law, Keith, what the plant actually was. He informed me that it was poison hemlock, and I was once again off on a plant quest!
Poison hemlock (Conium maculatum) belongs to the same family, Apiaceae (or Umbelliferae), as several other very familiar garden plants, including parsley and carrots. It is unrelated to the coniferous tree that bears the same common name, the Eastern Hemlock. Gardeners will recognize the finely toothed leaves and clusters of small, white flowers common on plants in this family. Queen Anne's Lace (Daucus carota), also known as Wild Carrot, is similar, with deeply cut leaves.
This similarity has led to some accidental poisonings, as people have dug the roots, believing them to be the edible wild carrot, or chopped the greens up and included them in their salads. It is very important to be able to identify them and avoid accidental ingestion! It is also recommended that you wear gloves and protective clothing if you will be digging or mowing this weed, as prolonged exposure to the juices can also cause skin sensitivity and some toxic effects. 
Hemlock actually gained some of its fame as a poison from Socrates, the ancient Greek philosopher. He was considered such a bad influence on the youth of the time, teaching them to question authority and challenge the status quo, that he was sentenced to death. The means of execution was drinking a concoction made of hemlock juice. Though the record of his death, as recorded by Plato, made it sound very peaceful and gradual, the actual affects of the poison on humans are much more dramatic and painful, and include seizures, diarrhea, severe abdominal pain, and respiratory distress prior to death. 
Both poison hemlock and Queen Anne's Lace have tap roots, similar in form to domestic carrots.The picture to the right shows roots of a hemlock plant that I carefully dug up on the farm, to check out the size of the roots. I did break off part of the larger root, but got enough to illustrate the general form.
There are a few key things to look for in determining whether a plant is Poison Hemlock or Queen Anne's Lace. Consult this chart to compare some of their distinguishing features:
Queen Anne's Lace
Smooth, hollow stalks with purple blotches or streaks,
especially toward the base of the plant
Fine hairs along the consistently green stalks. My son jokingly
asked if this meant Queen Anne had hairy legs!
Can attain heights of 3-10 feet,
depending on the age of the plant
Generally doesn't exceed 3 feet in height
Hemlock has many flower heads all over the entire plant, and may appear to have several umbrella-shaped clusters of flowers in each inflorescence.
Usually has one primary flower cluster at the top of the stem,
often with one red flower in the center of the cluster (the blood of Queen Anne)
Blooms in late spring. Blooms in summer and autumn. Scent:Unpleasant odor, both upon brushing up against it and upon crushing or bruising the leaves. This may be a defense mechanism to alert animals to its poisonous nature. It has been described as smelling "musty" or "mousy." Foliage smells pleasant and "carrot-y" when crushed or bruised.
Now that I've learned to identify poison hemlock, I see it everywhere as I travel. Be alert, and use caution when you come into close contact with it!
With the exception of the pictures listed below, all other images are my own.
Melody Rose (DG Member Melody): 3 images: Purple blotches on hemlock stem, red spot in center of Queen Anne's Lace, and hairy stems on Queen Anne's Lace
DG member Jonna Sudenius: Picture of full Queen Anne's Lace plant, demonstrating size