Fees for an ordinary payment on one network rose several times over for about six hours on Tuesday afternoon, then fell back (sample report, 5 of 6 checks: developing).
The reason is space: each block holds a limited number of payments, and when many people send at once they offer more to be included first. Payments with lower fees simply waited a few hours.
If a payment is not urgent, a lower fee usually gets through within a day. The amount you send does not change the fee.