Free Tool #1:
While designing and supporting embedded systems I am always in need of quickly finding component pricing and availability. I came across www.oemstrade.com website while searching for End-of-Life component crosses.
This website allows you to type in a manufacturers part number and it automatically searches through 34 different electronic components distributor's websites. Digikey, Newark, Mouser, Avnet, Arrow and Future are all included in the search (NuHorizons needs to get on board as well). This simplifies searching for "in-stock" components. I also just use this website as a part number checker to make sure I've entered the P/N correctly in my BOMs; if the part is found at some distributor chances are it is a valid part number.
Free Tool #2:
You don't have to be an RF Engineer to need PCB trace impedance calculation tools; with DDR & DDR2 memory traces requiring 50 Ohm characteristic impedances, Ethernet requiring 100 Ohm differential traces, and USB requiring 90 Ohm differential traces even the Embedded Designer is in need of calculating PCB Trace Impedances. I came across the Saturn PCB toolkit (http://saturnpcb.com/pcb_toolkit.htm) software package several months ago and I've been putting it to some good use. This tool uses IPC-2221, IPC-2251, IPC-2152, and IPC-2141 for calculation of: trace impedance, differential traces, via impedance, trace & via current capacity and much more. This tool has its limitations, the IPC standards don't take into account all the different field effects especially if you are exceeding the Trace height and width ratios, but this tool is a lot less expensive than a $15,000 Field Solver. All trace impedances should still be checked by your PCB supplier for accuracy.
Free Tool #3
I like to do a lot of hands on testing, but every once in a while a quick simulation will answer my questions about a circuit and I can save the trip to the lab for the next problem. SPICE simulation tools have come a long way over the years and as long as you have a basic understanding of what the outputs should be (so you know if the simulation is inaccurate) these tools are very helpful. I have been using LTSPICE from Linear Tech (http://www.linear.com/designtools/software/) for years now and I really like it. It is not as pretty or easy to use as ORCAD, but I have gotten used to the quirks.
Linear Tech provides LTSPICE with a library full of Linear Tech parts and some various passives. They obviously want you using their parts, but I've simulated Analog Devices opamps and Texas Instruments comparators by creating new components that reference the other manufactures SPICE file. LTSPICE is definatly worth downloading and giving a try. There is also a Yahoo News Group that specifically discusses LTSPICE activities and issues.
If you have any other Free tools that have been helpfully please add the links as a comment to this post.