I have used OSHPARK for several designs that I don't need quick turn around on. I have been very happy with the quality and price, especially for smaller boards. One project required a ½" X 4" board. I got 3 pieces for a total cost of only $10, including shipping.
OSHPark takes Eagle files. I use Eagle (paid version - some home projects turn into products for my ham radio/electronics side business).
I always create and send Gerber files though. I have had trouble with mixed up layers, missing silk screen items and similar problems when I tried sending native CAD files to circuit board houses in the past. So, I never sent Eagle files to OSHPark, but I know some people who have and apparently had no trouble with it.
@Susan: For home or amateur or even new professional work I would like to strongly suggest Eagle for schematic entry and PCB design. It is very low cost - $100 / $400 / $1000 versions. Very good EDA tool.
For simulation, free LTSpice should be very effective.
For test and measurement instruments, Newark has good noname oscilloscopes - around $300 and others instruments as required. For DMM Fluke is the best, but Extech and other are also good start.
Hobby electronics is lots of fun. As you earn more money, you can reinvest them in Agilent/Tektronics/Fluke and other software tools.
As we unveil EE Times’ 2015 Silicon 60 list, journalist & Silicon 60 researcher Peter Clarke hosts a conversation on startups in the electronics industry. Panelists Dan Armbrust (investment firm Silicon Catalyst), Andrew Kau (venture capital firm Walden International), and Stan Boland (successful serial entrepreneur, former CEO of Neul, Icera) join in the live debate.