I got a new phone and want to put the SD card from my old one into it. Should anything be done to it, such as formatting or deleting files? There is a lot of funky stuff on the SD card, from TWRP and Titanium Backup etc. On the other hand I'd rather not delete just for the heck of it as there's a lot of stuff and some I do want to keep.
There isn't a need to format it. However, depending on how the SD card is formatted (file system), it may at times not readable by the new device, in which case it is best to format it using the device if it has that facility or a laptop. FAT 32 is pretty much recognised across devices but be aware that it can't store files bigger than 4GB. As always, it makes sense to backup your SD card on your laptop, as you say data contained is important
In short, if the new device can read the SD card, don't bother
Additional information on compatibility of SD cards - Source
Should you decide to format and are unsure about the file system, information here should help you ( also consider which laptop OS you would want to work with ) - How many files can I put in a directory?