I saw a story on CNN Money today, via their partnership with Fortune, talking about what a great job the CEO of HP has done in streamlining operation, honest accounting, and generally turning HP from a mediocre company into one capable of weathering this recession. In such an environment, this sounds like a company I’d like to work for. So I’d suggest you check out their hiring page, especially if you have any computer/software/hardware experience. But, keep in mind as well that any large company–no matter what they do–requires substantial administrative overhead.
For example, as a writer, if I were to apply at HP, I would look for jobs for technical writers (people that write the instructions for their products, essentially) or copywriters (people that write advertising trying to sell the products). They also tend to be in far more markets than small companies, and thus, offering a job closer to you. That’s the advantage of larger companies.