Vim is my editor of choice. I use it for everything. I haven’t done any TeX stuff for many years, but I used to do it in vanilla vim, without any extra plugins and used a Makefile so I could run :make to build/preview the document.
Vim has built in TeX syntax-highlighting.
There are a number of plugins available that can help with your workflow when working on TeX documents in vim too.
Emacs is also great for TeX stuff. Like vim, Emacs can do pretty much everything. I haven't used emacs since getting problems with my hands, but the situation is very much the same as vim. It has built-in support for TeX and there are numerous plugins/extensions available that can aid your workflow.
I have used a few dedicated TeX editors/IDE’s in the past. Lyx, Kile and Texmaker are all really good. There are a number of others available, but I haven’t used them.