And import duties even apply on gifts. A friend in the States sent me some custom items he had made as a present and clearly marked them as gifts on the package. He also out on them a value of $100 on which I had to pay import duty etc.
In most cases, at least in my experience, it's not Customs Duties as such - I've never been charged actual import duty on anything coming in from the US, more likely it will be a bill for UK VAT at 20% plus the handling fee that the carrier (Royal Mail, Parcelfarce etc) impose to cover their "costs" for charging and collecting the VAT (and then the VAT on the handling fee that they charge for collecting the VAT....

)
Anything that comes in over about £18 in value - gift, purchase, whatever - is liable to have these charges, IF the parcel is stopped and checked... but as I'm sure we've all experienced, some randomly slip through with no charges because they don't seem to catch every one.
Whatever happens post-Dec 31st, I expect that the worst-case (as far as imports from Europe are concerned) is that we'll have to do the same with them - some will get checked and you'll be charged VAT plus fees, a few will slip through unchecked; to balance this, of course, we won't be paying the VAT at the sender's end, so if ordering from Germany we should buy VAT-free (so not paying the German VAT of 19% as part of the purchase price) but then we will be liable for the UK's 20% VAT plus whatever the carrier feels they can extort from us in charges.
Jon.