One was sacked and two resigned after managers at Neath Port Talbot council found that some staff were spending up to two hours a day on eBay.
Union officials, however, said the council had put "temptation in their way" by not blocking sites such as eBay.
Graham Jones, personnel chief at the council, said the council had a policy of allowing its staff to access the web for personal use in their own time.
The council has network filters in place to prevent access to pornographic sites and other unsuitable material, but no blocks on sites such as eBay.
The union said personal web access should be restricted to lunch hours by the council, and that filters should be extended to block extended use of sites such as eBay to prevent other staff from "becoming addicted".
Read more on IT risk management
People disposing of their old computers could easily fall victim to identity theft - even if they delete files or wipe the hard drive, warns Which? Computing.