Thunder Force 1: 1984 or 1985, made for many Japanese 8-bit computers. 100% overhead scrolling, bi-directional (?) shmup.
Thunder Force 1 appeared on:
1.) Sharp X1
2.) NEC PC-88 (aka NEC PC 8801)
3.) NEC PC 6001
4.) Fujitsu FM-7
5.) Sharp MZ-1500
see this thread for lots of info on Thunder Force I
http://forum.shmups.com/forum/viewtopic.php?t=369&highlight=thunder+force+sharp
Thunder Force II: made in 1988, originally for the 16-bit Sharp X68000 computer. it's the best version of TFII. later it was converted in downgraded form to the Sega MegaDrive | Genesis in 1989.
so what does the older Sharp X68000 computer version of TFII have over the Sega console version? at least 2 more levels (maybe more): one additional overhead level, one side scrolling level. better color (both pallete, and simultaneous on screen) more parallax scrolling (immediately noticable)
more weapons, clearer audio, especially voice samples. (the pilot says SHIT when you lose your last life) and more difficult gameplay.
for most people, the MegaDrive or Genesis Thunder Force II was the first Thunder Force game they played, as it was for me. I had no idea a better version of it existed on the Sharp X68000 until a few years ago.
Thunder Force III: released in 1990 for the MegaDrive | Genesis. this was the peak of the series for most of us. awesome game that did away with the overhead levels of part II. (and part I which hardly anyone in the west ever saw). Thunder Force III had amazing boss battles and parallax scrolling levels. who could forget seeing the wavey fire effects of the Gorgon level. holy fuck!
Thunder Force AC: the arcade version of TF III that has a larger color pallete, a few new levels, and two of the Mega Drive / Genesis TF III levels removed.
Thunder Spirits: the poor SNES port of Thunder Force AC with slowdown and bad color
Thunder Force IV aka Lightening Force: awesome game in most respects. very difficult. very long. tons of parallax scrolling. fun challenging. not quite as awesome as Thunder Force III was for its time though.
Thunder Force V for Saturn and Playstation. I dont know much about these other than that the Saturn version is much better quality overall. this is the verison you want to play. the PS version has some additional content, maybe an extra level or boss, but suffers from losing most of the parallax scrolling in the Saturn version.
edit: Thunder Force V releases go as follows:
Saturn - Thunder Force V
Playstation - Thunder Force V: Perfect System
Saturn Thunder Force V Special Pack (remixed music it seems)