I am thinking about volunteering at an animal shelter, but don't know much about them.
I think you should working at an animal shelter or pound is very fulfilling 
Are there all kinds of animals there or just dogs?
 Mostly dogs and cats, and sometimes sick or wounded wildlife. Though my shelter has birds as well.
Have animal shelters been around for a long time?
One of the earliest comprehensive measures was the "Georgia Animal Protection Act" of 1886. so they have been around a very long time 
Don't some shelters put animals to sleep if they can't find a new owner. I don't think I want to volunteer at one of those
You're right no-kill shelters exist, it is sometimes policy to euthanize sick animals but its only when the animal is suffering and in pain.
I have a big decision to make. Any other advice to help me decide?
dogs. Critics believe the new term "animal shelter" is generally a euphemism for the older term "pound". The word "pound" had its origins in the animal pounds of agricultural communities, where stray livestock would be penned or impounded until claimed by their owners.
United States & Canada.
In the United States there is no government-run organization that provides oversight or regulation of the various shelters on a national basis. However, many individual states do regulate shelters within their jurisdiction. One of the
Animal shelter
An animal shelter or pound is a place where stray, lost, abandoned or surrendered animals, mostly dogs and cats, and sometimes sick or wounded wildlife are kept and rehabilitated. While no-kill shelters exist, it is sometimes policy to euthanize sick animals, and any animal that is not claimed quickly enough by a previous or new owner. In Europe, of 30 countries included in a survey, all but four (Czech Republic, Germany, Greece, and Italy) permitted the killing of healthy stray