Can an employer not hire a woman due to her being pregnant?

Actually, based on the exact phrasing of your question, the LEGAL answer is YES, an employer may elect NOT to hire a woman based solely on the fact that she is pregnant.

EEOC regulations would make such a situation a violation of anti-discriminatory regulations but they only apply if the employer has more more than 15 employees. Otherwise, state law prevails.

It doesn't mean the employer is free from legal liability. Only that such a decision CAN be made.
No, Hippa laws...People do it anyways...

Of course there are some jobs that are dangerous for pregnant woman. (Flying in the third trimester, so no pilots etc., or painting, because of the fumes).
In most cases, no. The exceptions to this would be:

1. If the job required that the woman be exposed to things that would be harmful to the developing child and there are no other 'reasonable accommodations' they could make to eliminate those harmful things, they can refuse to hire her.
2. If the employer has fewer than fifteen people, they are exempt from Federal EEOC laws. There may be state laws that also say they cannot refuse employment on that basis, but with fewer than fifteen people, they are not beholden to the Federal ones.
3. If the person cannot reasonably accomplish the work that they are being hired to do because of their pregnancy, they can also be denied employment on that basis for the duration of their pregnancy.

Hope that helps!

No. Unless pregnancy is a bona fide disqualifying condition (heavy lifting or exposure to toxins) it's a violation of Title VII of the Civil Rights Act and you can sue for it. You'll even make money if you can prove you were not hired because you are pregnant.

Discrimination against pregnancy is sex discrimination, because only women get pregnant.
only if she cannot physically preform the duties she is being hired for.
no, but proving it was because she was pregnant is a whole different story

No they can not. She is considered a protected class. Equal employment opportunity (EEO) laws prohibit specific types of job discrimination in certain workplaces.

The Pregnancy Discrimination Act is an amendment to Title VII of the Civil Rights Act of 1964. Discrimination on the basis of pregnancy, childbirth, or related medical conditions constitutes unlawful sex discrimination under Title VII, which covers employers with 15 or more employees, including state and local governments. Title VII also applies to employment agencies and to labor organizations, as well as to the federal government. Women who are pregnant or affected by related conditions must be treated in the same manner as other applicants or employees with similar abilities or limitations.

Title VII's pregnancy-related protections include:

An employer cannot refuse to hire a pregnant woman because of her pregnancy, because of a pregnancy-related condition or because of the prejudices of co-workers, clients, or customers.

For more info or help filing a complaint:
Being pregnant is considered a disabilty. Women are in a new social class for at least nine months. In the long run it will pay off. A pregnant woman will do the work she is capable of. So hire her if she is qualified. Remember she is not going to be pregnant the rest of her life.
No, they cannot discriminate against a pregnant woman. And even if she were already working for them, they cannot let her go because of it either.
This is the problem that I am having, I found out that I am pregnant and my employer is trying to find a way to get rid of me.
They were NOT thrilled when I told them, and let's see...Miracles DO HAPPEN! Because that is what my baby is, a miracle...because we thought we could not have any more!
So, tell her to hang tough and if they give her stuff...tell her to get a lawyer!