Pretty sure I have the same problem as you. Mostly the older, lower leaves affected. New growth on top seems fine. More noticeable on underside of leaves. I'm not an experienced gardener but my google searches seem to suggest Septoria Leaf Spot. Would love for someone with experience to weigh in on that.

I have only two tomato plants - a big beef and a cherry tomato. I have only noticed these spots on the cherry plant so far. I'm using drip irrigation but wondering if our rain in northern California last weekend contributed to the fast spread.

I'm planning to throw all foliage that looks infected in the trash (which will probably be 80% of the plant). Then I'll spray with a fungicide and mulch to avoid splashing spores if we get any more rain.

More info here:
http://www.ct.gov/caes/lib/caes/documents/publications/fact_sheets/plant_pathology_and_ecology/septoria_leaf_spot_of_tomato_06-30-08r.pdf

Thank you dhopman.
Since I sprayed neem oil last weekend, it seems that the situation has not gotten any worse. would I still need to remove infected leaves?
Thanks
-andy