2 DUIs (2001, 2002); 1 driving without registration/violation of probation (2003). Probation has expired, all fines and penalties completed long ago. Haven't driven since 2003. Spotless record since, going to law school in the Fall.
Can I get it dismissed without an attorney?
You can file your own motion for a dismissal under Penal Code 1203.4, but you are probably better off with an attorney due to the probation violations.
You should also keep in mind that the dismissal, even if it's granted, has very limited value in a DUI case. It will still show up on your DMV record, and will count as a "prior" in any future prosecution, for ten years.
Under Penal Code §1203.4, a person who is granted probation can apply to have the case dismissed after probation is complete. This is sometimes called an expungement, but it doesn't really expunge anything or seal your record. The conviction is still a part of the court's public records, which will also show the case was dismissed. You still must disclose the conviction when applying to be a police officer or for certain other jobs, or if asked on an application for a state license or to run for public office. As I noted above, your prior DUI convictions could be used to increase the punishment for subsequent DUI convictions.
BEWARE of law firms that promise to "clear your record" and charge thousands of dollars. The process of filing a Penal Code §1203.4 petition is pretty simple, and you can do it yourself with forms available from the court clerk's office, especially if you completed probation without any problems. If you had a probation violation along the way, you may want an attorney's help, but the guys who charge thousands to file simple paperwork will probably overcharge you for that, too.
California Labor Code §432.7 says employers can't ask about any arrest that didn't result in a conviction, inquire about it from other sources or use it in a hiring decision.
Some attorneys interpret this Labor Code section to mean you don't have to disclose a conviction that was dismissed under Penal Code §1203.4, but I usually advise clients to disclose it, with an explanation that the conviction was subsequently dismissed.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
Another note: Although the DUI conviction will drop off your DMV record after ten years, it never really "leaves your record."
Failure to disclose the convictions, if required, on applications for employment or state licenses could result in getting fired from a job or denied a license.