There's always Windows Movie Maker (/equivalents) if you're on Windows. It's really not bad for basic editing. I remember hearing that Macs also come with a basic video editor?
There's Lightworks if you want more special effects (free version is limited to mp4 exports & needs to be renewed weekly). I'd recommend Filmora, but the trial version's watermark is just too much to ever recommend for trailer work. Blender (a free 3D modeling software) has some awkward video editing and export tools as well.
There might be better ones out there I'm not aware of. At the very least, there's dozens of miscellaneous freeware junk floating around from old college programming assignments.
If you honestly want to work with a lot of text and get some nice effects, etc. without dishing out money for a video editor, though, you might be best off just working in your game engine of choice. ex: Make a new branch, hard code the trailer effects there with the right timing, then record what happens. (That workflow isn't always an option, I know, but it is fun.)