Not continental Europe, but 3 weeks ago I bought a sandwitch, drink and a Vodaphone sim card at Dublin international, right outside Terminal 2. I paid cash for it. Came with 20GB of data. I never tried it, but apparently you can buy topup vouchers at retailers also for cash.
I converted my number to a bill-pay last week, and I had to submit proof of residence for that. I think they also asked for proof of ID (passport) and proof of residence status.