In the US keep in mind the Bank Secrecy Act.
You may trigger a Currency Transaction Report for cash transactions in excess of $10,000 in one day, a Monetary Instrument Log for checks purchased with $3,000 to $10,000, and a Suspicious Activity Report within the bank's discretion.
from: http://www.fincen.gov/statutes_regs/bsa/
These wouldn't prevent you from making a purchase, and you might falsify information sufficiently to avoid association with your real identity and drawing unwanted attention, but it's another hurdle.