Yeah, asking for letters is kind of an awkward fact of life, but a necessary one. Think of it this way - it is not only beneficial for you, but for the professor to write one as long as you are worthy of it. The better graduate school you can get into (and succeed in), the better it reflects on the department.
However, be sure to stay organized. Make your list of schools and make sure they approve it. For many of the schools, you will need to log in online and submit your letter requests, which your professors will receive by e-mail. Ask them when they prefer to get it - if you're applying to 12 schools, they're going to get 12 emails spamming up their inbox, so they may prefer it to happen overnight or on a weekend. You should do them all at one time unless your professor wants otherwise - keep in mind that for some schools, you cannot request letters until the application itself is complete and submitted, so be sure to have your application materials handy.
Also, many letter-writers will request a research summary or CV, especially if you haven't worked with them ina while, so they can be very specific in their letter for you.