Which careers have pension plans?

Depends on the employer, not the job duties/career. Very few places have company pensions any more other than some unions. Most have been replaced with 401K's or 403b's, where you contribute your own money, and many but not all companies make a partial matching contribution. This includes most health agencies.

Depends where you are and what benefits come with specific jobs. The more institutional the job the more likely there's a pension with it. Small businesses aren't likely to have pensions, and private industry has no obligation, but they might as a means of attracting talent.

"Careers" do not offer pension plans.

SOME employers offer pension plans. Not all health care companies offer pensions.

Pensions are becoming rare because they are extremely expensive to the employer, and they often carry huge commissions for pension salespeople, thus yielding less retirement money to retirees.

In general, pensions are only offered for government employees, or where there are super-powerful unions.

Most professional careers include retirement plans. Pension plans are optional and will vary depending on which company you work for.

Most government jobs have pension plans available, whether at the county, state, or federal level. There are jobs for all sorts of industries available in government, there's very few things you couldn't get as long as you have a degree. Most job descriptions will include information about pensions, retirement plans, and 401Ks and whether or not they offer them or this information will be on a company's website in the general section about employment there.