Oregon's is kind of weird, because the state has internal "highway" numbers and external "route" numbers, and the two, in many instances, don't match. For instance, internal "Highway 144" is OR-217, and parts of OR-8 and OR-47 make up internal "Highway 29".
The actual posted route numbers, at least the established ones, seem to follow some sort of loose grid. The north-south "primary" ones (1 and 2 digit) progress in odd numbers, generally increasing from east to west. OR-3, the lowest is in far northeastern Oregon, and the highest one, OR-53, is near the Oregon coast. (It is also worth noting that US 197 was at one point OR-23.)
The east-west primary ones use even numbers and tend to progress in four "strips". The first strip with the lowest numbers (OR-6 being the current lowest) are in western Oregon, increasing heading south (down to OR-46), then there's a strip for central Oregon, which is actually largely unused--the only ones currently are OR-66 and OR-70. (US-26 over Mt. Hood was formerly OR-50, OR-216 was once OR-52 and part of US-20 was OR-54.) Then there's two strips in the eastern part of the state, one finishing out the 70s, with OR-74 and OR-78, and then, farther east, OR-82 and OR-86.
There are a few aberrations in there as well. OR-37 is in eastern Oregon, the current OR-52 is designed to be a continuation of ID-52 (it was once signed as OR-90, which makes more sense). There's also a couple that retained the number of decommissioned US highways--OR-99, 99W, 99E, and OR-126. OR-138 and OR-140 are also kind of oddities, but I presume they have their numbers because they are near OR-38 and a hypothetical OR-40 (if there ever was one), but extend far enough that they cross several strips. (Both are in excess of 100 miles, making them the two longest state routes.)
The old "secondary" routes use 3-digit numbers beginning with "2". The dichotomy of those is a little looser, and I'm not entirely sure how it works. There are some spots that make sense (OR-211, 213, 217 and 219), and others that don't (OR-237 way out in Eastern Oregon). They follow the standard odd=N/S and even=E/W directionality, though.
And in 2002, the legislature passed a bill calling for the signing of the remaining ODOT internal highways that didn't already have route numbers--the system on many (but not all) of those uses a two-digit "county code" for the first two digits, except in the instances in which the number conflicts with an already-posted route, in which case they make the first digit "5". Annoyingly, those don't follow the standard odd/even system, though, as OR-131 is east-west primarily.
-Alex (Tarkus)