My home state of Maryland does not use the letters I, O, Q, and U on its standard issue passenger license plates. Presumably the I and O are not used to avoid confusion with the numbers 1 and 0, but I don't know why the Q and U are avoided. They do sound similar, but that is true of many of the letters that are used. Other states do not follow these rules. The data below shows which of these letters I have seen on non-vanity license plates from other states and gives some examples of plates using these letters. The standard format of the license plate is shown enclosed in parentheses where "d" stands for a digit (0-9) and L stands for a letter (A-Z). Examples are enclosed in double quotes.
Wikipedia has more information on standard issue license plates. Samples of current standard plates are available here, including Q's for CA, FL, GA, IN, IO, KS, ME, MI, MS, OH, OK, OR, RI, and TN; I's for GA, NE, and SC; and possibly an O for CT.
This site has some notes about invalid letters on standard issue passenger plates, including no I, O, Q, or U for Maryland; no O (or 666) for MS; no I, O, Q, or U for PA; and no I, O, or Q for VA.
Arkansas
While in Texas, I saw an Arkansas plate with an I.
Wikipedia has more information on standard issue license plates. Samples of current standard plates are available here, including Q's for CA, FL, GA, IN, IO, KS, ME, MI, MS, OH, OK, OR, RI, and TN; I's for GA, NE, and SC; and possibly an O for CT.
This site has some notes about invalid letters on standard issue passenger plates, including no I, O, Q, or U for Maryland; no O (or 666) for MS; no I, O, Q, or U for PA; and no I, O, or Q for VA.
Arkansas
While in Texas, I saw an Arkansas plate with an I.
California
(dLLLddd) All letters are used, but the I, O, and possibly Q are only found in the middle letter. The Q has an unusual shape. The first digit indicates the age of the plate (lower values are older).
"6RIT751", "3XOV871", "6SOX164"
Colorado
(ddd - LLL) Uses 0 and O.
Delaware
(dddddd) -- no letters.
Florida
Uses I, Q and U.
Georgia
(LLL dddd) Uses Q
"ARQ 4169"
Ohio
(LLL dddd) Uses I
"FIP 7374"
Kansas
(ddd LLL) Uses Q and U
"RQJ 882", "845 CUL"
Michigan
(dLL Ldd; LLL dddd) Uses Q and U, but not I or O. Does not use front plates.
"3KQ L39"
Ohio
(LLL dddd) Uses I and Q
"EIY 6441", "DEQ 7994"
Oregon
(ddd LLL) Uses Q.
"622 EVQ"
Nebraska
"SLI 061"
(LLL nnn) Uses I and Q
"GIQ 157"
Tennessee
(ddd - LLL) Uses Q.
"266-ZQM"
Texas
I spent four days in Austin and never saw an I, O, Q, or U.
Texas may be avoiding all vowels.
Virginia
(LLL-dddd)
"WLQ-804" is an old plate from 1989 that added new letters to expand available combinations