When I wrap my books, I use a tape by Scotch brand called Mailing and Storage tape. Most times, when I get books, they're taped up with the same kind of tape. However sometimes I get books that are taped with a tape that is more opaque and a little more...hm...not sure if this is the best way to describe it but...stretchy. It's a strong tape and it certainly holds up well but I have no idea what kind of tape it is. The first time I received a book taped with it, I thought it was Scotch tape itself but it's not. It reminds me almost of something like a first-aid tape. It holds up really well through shipping and I actually find it a bit easier to get off if I can get a corner of it up.

Any ideas on what kind of tape this could be?

Does it have visible fibers in it?  That is what I think is sometimes called straping tape or filament tape. 

3M Stretchy Tape.  It's great stuff, but runs in the $2.50-3.50 range.

We have bought a couple rolls of easy to remove tape (Scotch brand, I think) and I don't like it precisely because it is easy to remove.  It is thicker and it sticks great on the first pass around a book or package, but if the tape lays on top of other tape, it sometimes doesn't want to stick.  I picture this stuff gumming up the PO sorting machines something awful (or at least coming somewhat undone before reaching its destination).

Me personally....I prefer the cheap stuff.  It sticks like the dickens and I can use gobs without feeling like it's costing me excessively.

I think from what people are describing of the different types of tape it must be the #M stretchy tape.

I found it interesting that when I bought my packing tape at Staples that the Scotch brand was cheaper than the store brand--and had the same yardage, etc.