I've been interviewing a few new BSEE graduates for a junior engineer position, and based strictly on what we're looking for, here is some random advice to juniors/seniors:
Learn a real design program like Altium. Eagle is ok, but I think downloading the eval version and creating a few small projects would be valuable. Create the parts in the library, capture the schematic, layout the board, generate the gerbers and send them thru freedfm.com until they pass. Maybe even send them to someplace like Advanced PCB which has deals for students. Knowing current tools is important. I think you're much more likely to use something like Altium than Spice or Matlab (which are also good to know).
Which brings me to my next suggestion-- do some hobby projects on your own. Take one of your interests, look at some projects on the internet, and adapt one of them to create something original on your own. It gives you something to talk about at your interview, and shows that you have a real interest in electrical engineering. Maybe even bring it with you to the meeting. It doesn't have to be elaborate, but you should understand it well, and be able to talk about it with confidence.
Senior design projects are also good discussion topics. You should be able to talk about what you personally contributed. What tools were used, how did the device work, what challenges did you overcome, etc. In my recent interviews, it often seemed like someone else in the group must have done all the work because the candidate could hardly describe what the project did.
Learn how to solder. You should own a decent soldering iron, and be able assemble prototypes which used SMD down to 0805 or 0603. If you looking for a job that does any sort of design, then chances are you're going to have to do some assembly/troubleshooting of your own prototypes.
Get some experience with current microcontrollers. I have a preference for Microchip, but Atmel or an ARM variant would also be good. I know teaching the 68HC11 still has value, but knowing parts that are more commonly used for new designs will make you seem more experienced and valuable.
Networking is important. Lots of new products these day have some connection to the Internet. Understand TCP/IP and ethernet. MAC addresses, netmasks, ARP, default routes, NAT... Even getting into the upper layers might be good, especially HTTP.
Linux would be nice to know. Embedded Linux continues to grow. Knowing how to compile a linux kernel, build a file system, or whatever would be a useful skill.
Anyway, those are just my opinions. I don't think any of these suggestions take a lot of effort, but they would go a long way to helping you make a good impression if you're looking for a position in a design group.
-chris