I have done it and still do, mainly on ebay.
My son has done it and he sent several thousand dollars for one item.....no problem.
It is really buying from a decent seller, and with ebay one can have 'some'
idea.I have only had 4 bad buyers in nearly 10 years.
As for other websites, a lot are very good too, it's not worth their time to be dishonest.
Pay Pal is just wonderful to use, and gives you peace of mind...and a lot of the sellers(outside of ebay) where it really started, use it now.
I am not an online shopper by habit, but when it's cheaper this way, or when I need something I cannot find in the local shops, why not? I go for trusted websites, though. I used to be more skeptical a while back, but I am getting more and more used to it.
I think it's perfectly safe to do online shopping so long as the website is secure. When you go in to provide credit card details, it should be a secure site - https and a little lock symbol should appear in your top left hand box (where you type website addresses). That is how you know you are dealing with a secure and registered website. I would not give any financial details to a website not displaying this as a minimum.