Are taxiways numbered in a predictable order?
In the U.S., taxiway number/nomenclature is generally designed in accordance with FAA AC 150/5340-18F. Also, Engineering Brief 89 available here clarifies some of the information in the AC with respect to taxiway numbering/nomenclature. The two pages shown below summarize the guidelines for numbering (from Engineering Brief 89)

Also, note the general taxiway numbering/nomenclature schema for Los Angeles International Airport (KLAX) illustrated on the bottom of this page.  The letter "A" starts the taxiway nomenclature beginning on the south side of the airport and progresses alphabetically towards the northside of the airport.  Intersecting taxiways are numbered sequentially.

Airport taxiway nomenclature can be very complex depending on the airport.  Also, as modifications are made to the ramps and movement areas, etc., effectively designating taxi routes or other areas of the airport becomes challenging.

Finally, in the U.S., there is a taxiway numbering/nomenclature methodology that is framed within FAA guidance documents.  A close comparison of the design guidance with current airport layouts and taxiway numbering/nomenclature not only illustrates the complexity involved but also reveals, in most cases, a consistency that can be relied upon and proves to be extremely useful in actual practice. 

Excerpt from Engineering Brief 89 (two pages):