The following rules seem to apply to the current run of Alaskan license plates. Some of these rules are only de facto rules because they come from nothing more than direct observation. Others are from the applicable laws and regulations or from information from the DMV.
There are exceptions - I've also spotted [318EYE].
The DMV has confirmed that legislators' plates are the only exception.
I have confirmed with the DMV that the DA-DE series is reserved for disabled veteran use later.
See the exempt plates.
There are exceptions, but there's no way to specify this on the DMV's request form, and the DMV tells me that there's no way to enter this into the system, either. The first one sighted was the [ADM KDM] plate. I have also seen [KS N OS], [A NET T], [FSH LPS], [SELL IT], [HUMM DL] and [NYY FAN] plates. I have never seen a regular-issue plate with seven non-space characters. See the exceptions for photos.
John Carty has reported the [BYBY] vs. [BY BY] exception, but I have no photos yet.
The 999XXX rule is relatively recent; I have seen personalized plates on the road that violate this rule, including [318EYE], [555WRC], [747DRV], [747CPT], and [888WPS], though I haven't seen them in a long time, and they may have been revoked or may have expired. There are, apparently, exceptions to the XXX999 rule ([FLY130],[PRO454],[LIN168],) but they may use I and 0 instead of 1 and O, respectively.
Some people add their own punctuation. I have seen one ([10-24], with a dash) that MIGHT have been from the factory. I've seen accent marks, apostrophes, and one very impressive ampersand.
There are other procedures for obtaining these. Because of their role in helping out during the 1964 Alaska Earthquake, ham radio operators don't have to pay extra for ham plates.
John Carty suggests that it is likely that there are exceptions, because many ham radio callsigns, especially those from other states, can be difficult to recognize.
The DMV paper form for getting plates lets you specify spaces as characters, so you can create your own justification. This is not available on the DMV on-line form.
The most notable examples are the right-flush [OMA] and [RS] plates, and [SCAMMR]. see the exceptions for photos.
There are clear exceptions, but it's not really my place to point them out. :) The news page has some links to newspaper articles about this, though.