I forget who said this, but I think it's pretty accurate:
"Half-Life:Source basically just added ragdoll effects and bugs."
Generally speaking, the Source version of HL1 isn't worth it. In addition to the bugs, you also lose the ability to play mods of the first game. All you get in exchange is a slightly, very slightly, prettier game experience.
I would say Blue Shift and Opposing Force are worth a play through. Opposing Force is by far the better of the two expansions though, Blue Shift is cool but awfully short and lacking in variety.
Also, as Cat mentioned, a fan-made mod called
Black Mesa is coming out. (Valve asked them to drop the Source from their name) The trailer, released, last year, said it's coming out in 2009, but no news has been released since then. Personally I'm skeptical about a 2009 release date, but I'd be happy to be proven wrong.