When I don't want to give my actual information, I give a valid phone number that won't reach me or bother anyone else: a valid area code (often my own) + 555-1212, for phone information. That's mostly for online stuff, where there isn't a person I can tell "no thank you" or "I prefer not to give that out."
For email, anything-at-all@example.com (or .org or .net) is a valid email address, but any email sent there will be thrown away: those domains exist to be used when giving examples as examples in textbooks, on websites, and the like. A human is likely to notice that they're not being given your real address, but it'll get around "I can't process this without an email address" because you can say something like "OK, then, just give it store@example.com." (In theory, a programmer could set things up to reject those, but for random marketing stuff at a cash register, they're very unlikely to bother.)