This is akin to the pre-digital cheating discovery methods of finding a receipt in a pocket or noticing revealing purchases on bank or credit card statements mailed to your house. Even if you opt not to receive paper bills or statements, your spouse can receive or run across statements via e-mailed notifications, and may be able to peruse online statements if you share accounts, or, as mentioned previously, allow auto-login information to be saved on your computer.
Most companies e-mail statement notifications out to customers who have allowed it, and they often enough prompt you to switch from paper to electronic notifications for environmental and cost saving reasons. A cheating partner might opt for these, thinking they are safer than the physical evidence of paper. And truly, most e-mails of this nature don't contain too much itemized information, but they can be the breadcrumbs that lead to more detailed online statements.
If you have a hidden account or two, say for an additional mobile line or an extra credit card or bank account opened just for dalliances, there will still likely be a digital trail that leads to and from you via your computer or phone. So you can't assume an extra phone or gifts or clandestine hotel stays will remain secret forever. In the case of the phone, a prepaid or disposable phone might solve the statement issue, but the very existence of a second phone might serve as a clue to your significant other.