The main series goes in this order:
1. Elder Scrolls: Arena
2. Elder Scrolls II: Daggerfall
3. Elder Scrolls III: Morrowind
4. Elder Scrolls IV: Oblivion
5. Elder Scrolls V: Skyrim
Their is also a few spinoffs:
Elder Scrolls: Battlespire
Elder Scrolls: Redguard
Elder Scrolls: Travels (Released for the N-Gage)
Elder Scrolls Online (Not yet released)
You can download Arena and Daggerfall for free from the official website, but I recommend using
Arena Setup and
Daggerfall Setup because getting these games set up in DOSbox is a lot of work. I have not played Daggerfall much, but I did enjoy the time I spent playing Arena, I gave up after the second dungeon though as it was very clunky, difficult, and was requiring more time than I cared to spend on it back when I played it. The only other game I have played is Oblivion and I really like it. I have not spent a whole lot of time in it, but I completed the Dark Brotherhood campaign and it was awesome.
I would take MJMaranan's advice and purchase
The Elder Scrolls Anthology since it has all of the games from the main series.