I have used Paypal since my website launched, but have had disproportionate problems with failed/abandoned transactions as the order volume has increased. That has meant lots of manual processing of orders, cheque payments and phone calls from customers who have had problems (and, I expect, lost sales from customers who have just given up).
Although I usually try and follow up with an email to customers whose online payments have not completed (and often get the sales as a result), I don't always have the time to do it. Even then Paypal can refuse to play ball when an invoice is issued manually (typically when customers live overseas but have a UK bank account, or if someone else in their household has a Paypal account and insists that they do when they don't!)
I have just signed up for Worldpay so that there is an alternative payment method on the site. They have, or had until recently, a special offer for new businesses which effectively halves the normal set up charge and monthly fees. I should be having it integrated it into my site in the next week or so.
From the research I did with some of my regular customers, it seems they would prefer to have alternative payment options. They also reported a higher level of trust in Worldpay than Paypal which still suffers from its ebay association. Direct customer feedback helped me make the final decision (along with cost) but I suppose customer base expectation will vary depending on the type of business.
I know Worldpay had a major problem when upgrading their system last month, but as Sandra says, there are issues with all of them from time to time.