There are several reasons why I like the Elder Scrolls. These points mainly apply to the last three games in the series.
First: mods. Bethesda's games are the most thoroughly mod-able games I have ever known.
Second: open world landscapes. I love the fact that my character can actually run or walk from one end of their game worlds to another without traversing "maps" or zones."
Third: non-linear storytelling. Several story lines take place at one time. The main quest is only one of them. We can mix-n-match quests to suit the needs of our characters. We don't even need to do any of Bethesda's quests at all. We can invent our own.
Fourth: the mix of first-person shooter and roleplaying combat. Combat in the Elder Scrolls has always been a hybrid player-skill/character-skill system and I think this is one of its best features. While I like character-skill-based roleplaying combat and I like player-skill-based first-person shooter combat, I love the Elder Scrolls' fusion of the two.
Fifth: semi-classless character generation. Classes in Morrowind and Oblivion were not the restrictive, rule-bound classes we find in Dungeons-and-Dragons. They acted mainly as starting points, after which we could go in almost any direction we wanted. Skyrim has moved even further toward this classless approach.
Sixth: leveling through skill use. The Elder Scrolls' skill use system of leveling is, in my opinion, the most logical, most immersive, most intuitive roleplaying leveling system in existence.
Seventh: artistic vision. From Morrowind's Telvanni towers to Oblivion's Deadlands to Skyrim's breathtaking view of Solitude from a distance, the art design of these games have been, at their best, wonderfully creative. These games have been a joy to see and to wander through.
Eighth: Jeremy Soule's music.