Does 1800s have to have an apostrophe?

If you are taking about the years from 1800 to 1899, then it is a plural, so it is the 1800s. If you are talking about something belonging to the year 1800, then it is a possessive and so it uses an apostrophe. For example, you could have something like: 1800's summer was very good. It is very common to see people use the apostrophe in the wrong way when talking about years that way.