Luckily, so far, every doggie I have ever owned (okay just one) was small enough to fit in a small petflys carrier, which can be buckled into the car seat and stays pretty well... but my friends with larger dogs recommend both the pet lookout (with harness attachment) and just the plain old harness attachment that goes on a seat belt (which is properly secured keep the dog in place and do not tangle).
After seeing a link that showed what can happen in a crash if your dog was not strapped in, I vowed NEVER to let my dog run loose in the car. (that sherpanet thing looks like it would be comfy and work nicely for short trips). Also, if you have airbags you may want to think twice about the dog sitting on the passengers lap. And I never recommend the dog be sitting on the drivers lap, both because of airbags and just too plain distracting and hazardous!
I think there may be a link around here somewhere, if I can find it I will post it. The video shows two Crash Test Dummy Dogs - one restrained, one not- in the event of a crash. The poor unrestrained doggie gets completely tossed, while the other one (who could possibly still get minor injuries) was still in his general seating area with less tossing.