The Ys series chronicles the life of Adol Christin, a young man obsessed with adventure. Gameplay usually revolves around Adol, though his comrade, Dogi, is a frequent companion in his travels. More recent games in the series include several other playable party members.
They're connected in that they take place in the same setting, but they're not connected in the sense that playing games before is necessary to understand later games. Ys I & II are connected directly by story. The rest can be played in basically any order, as far as story is concerned.
