When you're asked for your credit card before renting a car or checking in at the hotel, they're often not just taking an imprint. Travel expert Peter Greenberg points out that, more often than not, a hold is being placed on your available balance for the entire estimated bill. While this can be fine for credit cards, it's a bigger problem with debit.
The hold occurs because the hotel or rental car agency wants to protect itself by ensuring you can't overspendn. Basically, if the money isn't available for use there's no chance you'll use it. If you provide a debit card, this effectively reduces the money in your bank account before you owe it.
While this sort of hold is easily reduced on a credit card with a quick phone call, it can take much longer with debit. If your bill turns out to be less than expected, you could end up without access to your own money.
This is most easily remedied by using a credit card when asked, but if you don't have one or don't want to use either just ask for alternatives. You may be able to get the amount of the hold reduced or even eliminated if you offer to pay partially up front (e.g. for the first night). If you end up using a separate card for the hold, be sure to ask the hotel to have it removed once you pay or it could persist long after your travels have ended.
Travel Tip: Blocking Charges For Hotels & Car Rentals [Peter Greenberg Worldwide]