All right, so... this is driving me just a little crazy. I am a doc and I do primary care (but I don't treat any of you, so please take what I write with a grain of salt). This is what the general recommendations are: (link)
http://www.journals.uchicago.edu/doi/pdf/10.1086/314053?cookieSet=1
Critical factors are type of tick (I'm pretty sure the one in your picture was a deer tick), time of attachment, and (what nobody's mentioned so far) whether you were in a Lyme-endemic area.
(another link)
http://www.aldf.com/usmap.shtml
People are pretty good at telling whether the tick is big or small, I think. So, if it was a small tick, in less than a zillion words, I tell everyone to watch for symptoms. The rash, while not universally there, is there in most (but not all) cases if you watch closely. And it's BIG, like many who have had Lyme here have mentioned. It's not just a little spot. If it's been more than 24 hours that the tick is attached, and they were in CT, RI or SE MA, I tell them there is a very real chance they will need to call me back. If they picked it up in another area, I tell them to worry somewhat less. If the tick was attached <24 hrs, I tell them to worry a lot less.
If there are symptoms, like a rash bigger than a quarter, I go ahead and treat. For a full course. (typically 21 days). 2-3 days of antibiotics has not been proven to help at all. Can it hurt? Sure. You could get an allergic reaction. You could (though the risk is much smaller) contribute to antibiotic-resistant infections in the future.
What does testing the tick do? Well, it tells you whether the tick should have gone to see its doctor for antibiotics. An infected tick does not mean you are infected. That's why they don't recommend it. Plus, it's expensive.
Hope this helps. Back to my alter ego.
Weatherman