Using your credit card online at reputable vendors is no different really, than handing your card to the guy behind the counter at your local sporting goods store. Much safer online, IMHO.
Keep in mind; most credit cards have built in fraud protection, so you aren't liable for fraudulent charges. This is better protection than Paypal. Paypal does not guarantee recovery of funds due to fraud. Ask me how I know this.
Also, I'm one of those guys who pays almost all of his bills online, most with my Visa debit card, and the rest with a deduction directly from my bank account.
I have never had one single problem.