Well I technically haven't worked as a EE yet (though I have my BS in EE, but I'm going to graduate school in the fall), but from what I've seen, the field is extremely diverse. For example:
Signal Processing: You might design some DSP algorithm for something.
Digital Circuits: You might design and layout some logic for a processor. You might design an ASIC in Verilog or VHDL.
Analog Circuits: You might design an amplifier for a cell phone.
Devices: You might work for a fab company designing a new MOSFET process.
There's also optoeletronics, which I'm less familiar with in terms of jobs.
Unless you've taken some EE courses at the college level, you probably have no idea what the above actually entails. Basically, every electronic thing you use had to be designed by some EE, and every sub-part also had to be designed (e.g., you might design a chip, or you might use a chip to design something bigger, or you might design the components used in the chip).