と and や are used to connect two or more nouns.
Most of the time, と can only be used for a fixed number of items like:
We need a keyboard and a mouse.
But や is used when there is a variable/unknown length like:
We need a keyboard, a mouse, and probably LAN cables too.
や can also have the sense of "OR" or "AND/OR" as in:
I haven't tried sushi and/or sashimi in Japan yet.
But と only means "AND":
I haven't tried sushi and sashimi in Japan yet.
そして is used as a conjunction between two phrases and has the sense of "then ..."
～たり is used to connect two verbs and is used in the sense of giving examples, like Lukman mentioned in the comments:
～くて is used to connect two adjectives like:
She is pretty and has wonderful style.
And yes, ～し～し is used to connect two adjectives, with exclusive positive or negative senses:
This room is clean, spacious, and also well partitioned, so most of the people like it.
That room is (a bit) dirty, (kind of) dark, and far from the station, so nobody bothers to rent it.
～も is normally used in the sense of "too / also", but sometimes it is used in the sense of "AND":
I'd like to have this, that, and also that one, basically everything.
And there are some more forms like ～かつ～ ("plus ..." or "not only ... but also ..."):
necessary and sufficient
Also, 及び, 並びに, ともに, and おまけに have a similar usage to "AND".