This answer comes from someone who has been a professor who has been asked for many reference letters, and also a hiring manager.
Unless you're applying to graduate school or specific programs which require letters of recommendation, asking your professors for letters that you're quite unlikely to use (see "How important is a recommendation letter for the employer?") is not the best idea. However, asking them to serve as personal references in your job search is a great idea -- if they've supervised your work or otherwise have a good relationship with you and can speak to your great qualities -- and for that you just want to secure their agreement as soon as possible.
When asking your professors if they'll act a reference, be sure to give them an idea of the types of positions you're applying to, and a sense of how many and how often your referees may be called upon to answer questions about you and your work. Many times your professor will have ideas about narrowing/focusing/targeting your job search.
If you are applying to jobs or programs that require letters of recommendation rather than conversations between HR/hiring managers and your referees, then you should approach your professors as soon as possible and give them as much time as you can possibly afford to give them, because -- wonderful though I am sure you are, you're not their only student looking for letters of recommendation ahead of graduation (although those students applying to graduate programs probably got their letters in the fall, so the herd is thinned a little!). When you ask for a letter, give your referee as much information about you (don't assume they remember all your great qualities or work) and your future plans, so that they can write a letter that is actually about you and your work and not a generic form letter. It is often very helpful to the letter writer to see examples of the specific job ads you plan to answer.
