Phone/tablet app purchases
Adding to @Chris H answer about damage limitation
Online purchases could include phone/tablet app purchases, which could be an issue if you have children or you are a victim of fraud.
First link from googling "Kid racks up almost $6,000 on Jurassic World in-app purchases"
Adding to @Michael C. Answer
I think credit cards perhaps can make it more difficult to budget, if you are more lazy/have limited savings. These might happen more long term if you don't keep track of your spending.
I.e. If your credit limit matches your monthly income, and if you pay off your card each month, I think it is harder to overspend as you don't have more credit available than you can afford to spend.
However this is countered by that, a slightly higher credit limit may help to avoid fees from exceeding your credit card limit.
I think due to that some/not all purchases are instantly "banked", i.e. the shop might send all of its monies to its bank at the end of the day or something like this, so you can just keep spending not realising you have exceeding your credit limit and get hit by fees.