I've been seeing these occasionally for years and wondering what in the world they were. Typically they land on your arm as you're walking down a trail in the afternoon. They're somewhat flattened, with stubby legs, and at first sight they look like some strange "winged tick", though one quickly notices they're six-legged.

At last I think I figured out what they are...Deer Louse Flies. From what I've read, we have two species in California: Lipoptena depressa and Neolipoptena ferrisi. According to Powell & Hogue(1), L. depressa exhibits "V-shaped lines on the upper surface of abdomen" (see this image), whereas Neolipoptena ferrisi does not. Unfortunately, the top of the abdomen isn't visible here (and I didn't know to look for that character when I saw this guy).

Here's a quote with some natural history info on these strange dipterans, from "Insects of the Los Angeles Basin" by Charles Hogue (2):

"Occasionally, a person hiking or working in mountainous areas will notice a small (1/8", or 3 mm, long) flattened brown fly that has landed on his skin or clothing. Looking much like a winged tick, the fly clings tenaciously or crawls sluggishly for a moment before flying away. This is one of the two common local species of Deer Louse Flies (Neolipoptena ferrisi or Lipoptena depressa), which normally live as ectoparasites on deer. ... Upon successfully finding a deer, it immediately crawls through the hair to the skin and begins to suck blood. Here it remains as a permanent parasite, soon losing its wings through wear. ... All Louse Flies are blood suckers, although none feeds regularly on humans. They may transmit disease between wild animals but do not to and between people."