Yes, we've been buying online for 15 years, mostly online these days, and yet to have any issues - knock on wood.
Unless we're buying something perishable or something that MUST be tried on (e.g. shoes, but not clothes IME) - we're far more likely to buy online. Brick-n-mortar stores are far less efficient (more time, less inventory, crowds, driving/parking) for most things to me.
Tangent observation on online buying:
I suspect we're more brand/store loyal than ever before as a result. In the old days
when we bought exclusively from brick-n-mortar stores, we were probably more likely to look at unfamiliar brands/stores because we could assess the quality first hand. Now since we're buying with little more than a picture & brief description, we're much less likely to try new stuff - so we stick with brands/stores we already have good experiences with. I only buy one brand of running shoes, most of my clothes come from Lands End, LL Bean or REI, and my boating gear comes from a narrow group of brands - just examples.