Are you talking about tablet organisers where each 'cell' has a number of different medications in it for different days and times of the day? Or are you thinking of the blister pack that many individual medications are delivered in, with a single tablet in each 'cell'?
I don't use the former method of arranging my medications, but if you are talking about the OEM blister pack, I would not recommend removing the medication from these until you are ready to take the dose you need.
While travelling to Europe, I keep all prescription medications in their original packaging, with the prescription label on any box, etc. I carry a copy of the script as well. Once I arrive, I remove as much of the packaging as I can, and place the blister pack sleeves of individual medications in their own zip-loc bag, cut the prescription label from any external packaging, and place that in the bag with the medication.
Normally I carry a small quantity of non-prescription medicines that I know I can get over-the-counter. You do need to be aware that what might be considered OTC in NZ might not be so in Europe.
Any complementary medications I will put in a labelled zip-loc bag, with a small sachet of silica gel. While these are easy enough to get in Spain and Portugal, the amount I need isn't that large, and I am happy to carry enough to avoid having to search them out along the way.