Just to clarify. I only addressed the question that the OP asked , rather than cover all the regs . for trailers.
A jet-ski or boat trailer will not need them ,as Fred said ,as they are under the 750 kg limit. They do need registering though if you are using the trailer for business use. For private use they are covered under your normal road insurance.
Re-registering a 3,1/2 tonne trailer , or one over the 750kg limit , is difficult & it has to be a manufacturer that is homologated for use in Europe. It's not really worth it unless the trailer is worth it , & you are able to be re-registering it as a personal goods & chattels . I:E within 30 days of your first padron , therefore without payment of any tax. It is possible to do without a certificate of european conformity but
A) you need to know what you are doing B) you need an ITV station that is helpful & C) an engineer that on that day is accomodating & knows the law.
I have re-registered some 750+ trailers & it varies as to who manufactures them . The chassis /Vin number has to be stamped on the left hand chassis rail when viewed standing at the ball -hitch looking back. One manufacturer stamps it ,but not in the correct size ( 8mm or bigger ) unless they know it's going abroad. Ifor Williams don't stamp it on the chassis at all ( they have other , undisclosed ,methods of ID on the trailer ) unless you tell them it's going abroad or they've manufactured it for export.
If your trailer does not have it's chassis /vin number starting with EC*/ & then followed by 8 or 10 numbers then it's not going to be able to be done at all.
The last Ifor williams that we re-registered for a friend cost 300 euros in total. He took it back to the UK to pick up his mini-digger & on the way back was stopped twice in Spain.