Yes, a lot of options here. The simplest is to do what @RyanReese mentioned, using PHP includes. (I put together an explanation of what they are and how to use them a while back that might be helpful.)
The next step up would be to create a single page template that you call into all your pages. Here’s a nice example of that: PHP include menu & class active CSS - #7 by system I’ve been using this method lately and love it.
Then you get into CMS territory. There are some really nice “flat file” CMSes around these days, like Statamic (not free) and Kirby (free) that do what you are looking for without needing a database. Slightly more geeky is the Jekyll option that @bpartch mentioned.
Ultimately, 'sup to you what you decide to do. 