I don’t sip the LaTeX Kool-Aid, I chug it. The combination of my hatred for Microsoft Word and the need to write papers and slide-shows heavy with equations made this a marriage of love and not convenience. I’ve read many threads on which LaTeX editor Linux users prefer, and I’d like to toss my two cents into the conversation. My vitals: I use Debian+LXDE, I am not a computer programmer (which affected my experience with Vim), and I’m not much of a Linux user. Here’s a list of what I’ve used and I feel gedit is hands down the best.
1. Kile. In 2008 when I first began searching for a LaTeX editor, Kile appeared to be the most popular and the most polished. Since I was new to Linux, I didn’t mind the Qt libraries that are needed for Kile. Kile is a very solid LaTeX editor, but as I’ve evolved from GNOME -> XFCE -> LXDE, I have both put a premium on lightweight desktops and learned to really dislike KDE. I have never gotten it to work correctly, on any computer. If you like KDE, Kile is for you, but I hate KDE and I won’t make an exception for this very good program. Also, as of the last time I used Kile, there was no auto spell checking, and I need auto spell checking.
2. Vim. The next time I set out for a LaTeX editor, I added the constraint that it couldn’t be written in Qt. This eliminated Kile, TeXMaker and TeXWorks. And Vim was the most popular amongst more experienced Linux users, which I thought I was. I used Vim for about 6 months, but ultimately it defeated me. First, as noted above, I have never been a computer programmer, and I’m too old to learn the keyboard shortcuts. And you can’t use a mouse to highlight text for cutting and pasting. And while the Vim addons manager package for Ubuntu is nice, I always had to tweak something in the .vimrc file, either for Vim to recognize a .tex file or to compile beamer class files. If you know Vim and like hacking away in the terminal, I’m sure this rocks, but I suck at both. Also, no auto spell checking.
3. Gummi. Gummi is a very new editor, but has a lot of promise. It appears lightweight and has some nice features, but as of this writing there is no auto spell checking. Once again, I can’t spell for dick.
4. LyX. I have only tested LyX and hated it , but other people seem to love it. Here’s why I don’t recommend it: 1) it’s in Qt so that’s strike 1, and 2) it’s WYSIWYM, which defeats the purpose of using LaTeX to begin with, I’m using LaTeX because I’m a document control freak. If you need the functionality of LaTeX, do yourself a favor and learn LaTeX.
5. gedit. Is the winner for best Linux LaTeX editor, in a landslide. First, it’s in Gtk, so it fits into my LXDE lifestyle. Second, it’s easy as hell to install; pop open synaptic, check select three packages (gedit, gedit-latex-plugins, and gedit-plugins) and you’re done. Gedit will recognize .tex files immediately, and compile to whatever you like. Adding the extra plugins package adds bracket completion and word completion. Combine this with an already very robust text editor, and you have the easiest, most powerful LaTeX editor available. And gedit has auto spell checking capabilities.
Rusty Shackleford's Library Card 
G-Edit is great! It’s like Notepad++ with a compiler. Thanks for reminding me it exists. I used to use G-Edit back in college when I didn’t any compilers readily available on my budget. My only qualm with using it these days is you can’t view your code in design mode. You have to compile the code, upload it to a web server or have a web server running on your development box in order to preview it.
Emacs + AUCTeX
I have tried EMAC+AUCTeX, which is also very popular amongst message board posters, but if you don’t know EMACS (like if you don’t know Vim) you’ll want to kill yourself before you finish your first paper.
I love Gedit with the LaTeX plug-in. Like you, I’m a doc-control freak – I LOVE html and LaTeX for that simple reason. It’s also why I loved WordPerfect – you could control everything using hidden codes. But I digress.
The deal-breaker for me with Gedit is that (I truly grieve) that I cannot customize the keyboard shortcuts. Sorry, but Billy Gates’s CUA interface just sucks. Whatever editor or word-processor I’m using, I immediately install a set of WordStar-like control keys for fast editing with the alphanumeric keys only. I can do this in Word, WordPerfect, OpenOffice, Lyx, jEdit, etc. But not in Gedit. (And I can’t get jEdit to compile .tex files, yet.)
If only there were a cross-application keyboard macro program for Linux Mint – similar to the old Borland Sidekick. (And, oh yeah, not one that requires me to learn the Python language.) Sigh.
Gummi now has spellcheck. The preview pane that compiles the PDF for you on the fly is priceless. It is quite lightweight, and I haven’t had any issues with it, even after typesetting a literary magazine. Gummi has my vote.
I used kile with Ubuntu and Fedora and I install with apt-get and yum. In both case the spellchecker works fine (including spanish, in my case, installing the language support, I don’t sure now but I think was aspell).