Your account number is on every checks. Checks are usually prefered because in the US you can cash them immediately and online.

Of course, YMMV. I've experienced both the US bank system and the EU (France) bank system. Even if Americans are very critical of our banks, no fee (usually) for anything, reduced red tape, and credit cards that are on your side won me over. When you take account of cash back and interests on checking, you've usually a cash positive relationship with you bank. Good luck finding that in Europe.