Also, are there any states that do not number exits on such freeways?
I think numbering exits on non-interstate freeways seems to be the exception in most states. Iowa is the only state I am aware of that consistently numbers the exits for almost all freeway segments.
As for listing other states:
IllinoisFull Freeway* IL 6 (has exit numbers)
* IL 255 (has exit numbers)
* IL 390 (has exit numbers)
Freeway segments* US 20 around Rockford and again around Freeport (no exit numbers)
* US 34 around Galesburg (no exit numbers)
* US 41, multiple segments in Chicagoland (no exit numbers)
* US 50 near the Indiana border (no exit numbers)
* US 51 south of I-72 in the Decatur area (no exit numbers)
* US 67 around Jacksonville (no exit numbers)
* IL 38 (no exit numbers)
* IL 53 (no exit numbers)
* IL 83 (no exit numbers)
* IL 92 in Moline (no exit numbers)
* IL 137/the Amstutz in Waukegan (no exit numbers)
* IL 336 Super-2 segment around Macomb) (no exit numbers)
* IL 394 (no exit numbers)
MissouriFull Freeways* MO 364 (has exit numbers)
* MO 370 (has exit numbers)
Freeway Segments* US 36 with multiple segments (no exit numbers)
* US 50 with segments around Jefferson City and into the KC area (no exit numbers)
* US 54 with multiple segments (no exit numbers)
* US 60 with multiple segments (no exit numbers)
* US 61 with multiple segments (no exit numbers, though I thought there was once an Exit 269 at I-70)
* US 65 with multiple segments (no exit numbers but does have enhanced mile markers on Springfield area and Branson area segments)
* US 63 with multiple segments (no exit numbers)
* US 67 with multiple segments (no exit numbers)
* US 71 segments in the KC area (no exit numbers)
* US 169 in the KC area (no exit numbers)
* MO 5/MO 7 around Camden (no exit numbers)
* MO 9 in the KC area (no exit numbers)
* MO 13 near Lexington and a few bypasses between Clinton and Springfield (no exit numbers)
* MO 21 in Jefferson County (no exit numbers but does have enhanced mile markers)
* MO 76/former MO 465 section (no exit numbers)
* MO 141 with a couple short segments in the St. Louis area (no exit numbers)
* MO 152 in the KC area (no exit numbers)
* MO 179 (short segment around Jefferson City (no exit numbers)
* MO 210 in the KC area (no exit numbers)
* MO 249 in the Joplin area (no exit numbers)
* MO 360 in the Springfield area (no exit numbers)
* MO 367 in the St. Louis area (no exit numbers)
* MO 752 for a very short segment around St. Joseph (no exit numbers)
* Forest Park Parkway through Clayton (no exit numbers)