If you are having problems with mods or with your install, please refer to the mod pages, your load order, and your patches before considering your install broken. Not all of them will work with only the base game installed. All mods listed here will work with all DLC installed. Some mods require you to download different files depending on which DLC you do or do not have.
When downloading, pay attention to the files you are grabbing.
Please read all mod pages before downloading and installing mods. The other issue I had was my own fault, forgetting to install a patch after downloading. The first issue was with a largish “expanded territory/quest” mod that caused CTDs for me, presumably due to known conflicts with one of the DLC. I only had two real issues when testing out all of these mods (and a lot that didn’t make it). As a user pointed out in the comments below, Fallout 4 is a lot more forgiving when modding than any previous Bethesda game. This guide is intended to be a list of mods that work well together and enhance the Fallout 4 experience without straying (at least not too far) from the unmodded game, gameplay, and lore.