I was happily folding up my cardboard box when the question hit me...is this tape recyclable? For once, Google couldn't answer my question! The best answer I could find was this article, that says it depends on your local solid waste management department. Some accept the tape, others require it to be removed. So, I scolded Google for not knowing the answer and called up someone who would; the City of Santa Fe Environmental Services number (here's their website). I got the answer to my question quickly: in Santa Fe, it is perfectly fine to leave the tape on your cardboard boxes.
But, this rule doesn't apply to all of New Mexico. Some solid waste authorities will compost the boxes, where tape is definitely a contaminant. The best way to know for sure is to call your local environmental services or solid waste authority and ask! So, open those boxes with joy, make sure they are dry and flattened, and put them in your blue bin!