The apparition of the first consumer-level dual-core processor is probably a landmark in the microprocessor history. This means that it has become really hard to make single-core processors faster for general processing. That’s why CPU designers like Intel decides to put 2 processors in the same chip.
So, concretely, what can you expect from a dual-core Pentium 4 ($)? Quite frankly I don’t expect much more. In fact out of the box, I expect it to perform mostly like a single-core P4. Why? Because most applications do not use multi-threading: a software mechanism to exploit multiple processors.
Until software makers start to use multi-threading widely, you will get a better operating system response (windows ($) is multi-threaded), and you can expect a boost in niche applications like video compression, but that about it.
More specific processors such as the Cell from Sony/IBM/Toshiba can outpace a general purpose CPU for specific tasks (think math), but they are not really that much better at doing general tasks.