It also depends on the work you are doing. If you are working under an industrial exemption then your company can protect you from Errors and Omissions claims.
If you stamp something, then it gets a lot harder. In New Mexico, I got my P.E. while working for a multi-national company. The attorneys at that company advised me that I could not stamp anything for them while employed unless I was willing to accept all liability (without insurance) and that they were not allowed to even contribute to my legal defence (one of them said that I couldn't go to court on their time, I would have to take vacation, I think he was probably over the top).
Read the admonition in my signature--talk to a lawyer.
Lburg..as others noted, it depends. Most companies indemnify their engineers for errors and omissions; however, in many states, the engineer may have joint and several liability with the company, so yes, they can sue you and yes, you can be held liable.
Should you rush out and get E&O insurance on a personal basis? I would not. I have worked for large and medium sized engineering firms and have owned my own firms. With my own firms, I have (and have had) E&O insurance for the company that covered me. The same was true of the firms for which I worked, and I work in a state that allows the engineer to be sued separately for engineering acts.
To follow on Ron's comment, if you work for a company and that company has insurance, it might be to your advantage NOT to have personal liability insurance even if in your location/line of work you have personal responsibility.
The logic is that suing you is expensive. If you have insurance, it is worth the bother and the expense to sue you in hope of getting some money from the insurance company. If you have no insurance, they could sue you but it is unlikely that your net worth will cover even their legal fees. Perverse, isn't it?
What does a plaintiff have to gain by suing an engineer? Nothing. Lawyers go after deep pockets so it seems natural to sue the company because: 1) large companies might settle out of court to avoid bad publicity. 2) Comapnies are either/or: well insured or have deep enough pockets that the lawyer has reasonable expectation to get paid.
In my home state, individuals are routinely chraged in a lawsuit along with the companies they work for.
I think it gives the lawyers a little something to negotiate.
In my area of the Southeast US, if a lawyer is suing a company, there is no extra cost or effort to add the PE to the lawsuit. The PE is often added not to actually collect any money, but to provide the threat that they may actually go after your personal assets. This is often done in hopes of getting that PE to testify against his employer on the condition of being separated from the suit. I have often seen employers and insurance companies go out of their way to help/protect their PE to keep him from flipping to the other side.