So a 'normal' person going on vacation, traveling for work, visiting a city just across the border will have fee-less roaming.
But you can't go to Romania, buy a SIM and use it here indefinitely.
You can also order them online for delivery to a specified address, they don't seem to check whether it is your home address but mine is paid using a French bank account which may help.
Regular subscriptions not, that's relevant for invoicing (as you can buy things through these subscriptions, it is pretty much like getting a credit card, hence asking for photo ID is entirely reasonable.)
No ID checks at either. Felt nice.
My current operator is Virgin, and that didn't require ID etiher, although since I already had a home internet account with them, that may have been why (no idea if new customers need ID). I did not need ID to setup the original home broadband account though. They obviously have my address and billing details, but they never had any proof that I'm who I saw I am. My previous phone provider was Three Ireland and they didn't require any ID either.
All of these except my Virgin SIM are/were prepaid. It seems that prepaids don't always require ID (and having postpaid/bill phones require ID does make sense).
In Germany you can buy SIM cards on the local supermarket, no ID requested.
They even requested your ID for SIMs you already owned and eventually disconnected all the unidentified.