There is a small hand-held tool called a laminate trimmer. I bought a PC unit for about $100, IIRC. For through holes or recesses which are over 1/8" deep I use a 1/8" spiral downcut flush trim bit that has a small brass sleeve on the end that acts as a guide. If they're right at 1/8" deep then I use a different bit that's 1/4" in diameter and has a single cutting edge and a flat bottom that's just under 1/8" thick. Smaller than that, and I cut my through hole first, use a rabbeting bit of the right size in my router to cut the recess in the cabinet, and then use that same bit at the appropriate depth to trim the veneer afterwards. You could even only cut the through hole and then cut out the recess after the cabinet is veneered.
You can see what the spiral downcut bit looks like (it's the top pic):
http://www.routerbits.com/cgi-routerbits/sr.cgi?1128460012_30912+98Here's the laminate trim bit that I use for the shallow recesses (it's the bottom pic):
http://www.routerbits.com/cgi-routerbits/sr.cgi?1128460012_30912+2Let me know if you have any other questions.