I've been using PayPal since its very beginnings, back when it was still X.com.
What do I think about them? I hate them. They cost too much, their customer service sucks, they are very heavy-handed with other people's money and play fast and loose with legal semantics pertaining to that money. Worst of all, they treat established sellers like idiots, by saying things that are simply not true and expecting the accountholder to not know any better (eg. when I had a 21-day hold put on my incoming payments, their FAQ on the matter says this is standard practice with merchant accounts, which is nonsense that anyone who has ever had a merchant account knows is nonsense. So why they would say such a thing is beyond me.)
Why do I use them? Only game in town for rapid deployment (ie. I can set up processing on a new site with a few clicks) and because consumers trust the logo. They are very easy for new merchants to get approved, and they integrate well with eBay and other platforms. Not much other upside to them, really.