I have recently had two attempts made against my own accounts while dealing with various Internet sites. On one occasion, I attempted to purchase an item from what appeared to be a legitimate site. I made the purchase using payment via my PayPal account. After about a week, when nothing appeared in the mail, I began to have second thoughts. After reviewing the site a second time, I realized that it offered no business address or phone number. My emails went unreturned. I voided the purchase, and luckily PayPal refunded my money after the web site also failed to answer their emails.
A second recent problem came when I stupidly allowed my security account to lapse for a few days. I immediately picked up several viruses and unwanted spyware which compromised my credit card. I was forced to cancel the credit card and change all of my passwords. On another occasion several years ago, a bogus payment receipt bearing what appeared to be proper eBay authentication appeared, and I foolishly responded with payment, using my credit card. Within hours I was contacted by the credit card company; someone was trying to make a $1200 purchase at an out-of-state Wal-Mart with my card number. Luckily, that purchase was also invalidated. On yet another occasion, someone hacked into my eBay account and attempted to sell items without my knowledge.
So, the personal identity theft issue is my biggest worry with computer crime.