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Can't speak for the 8 zillion client apps out there, but in the web UI, if you click on the "in reply to @soandso" text below one of those responses, it'll bring you to the original tweet.

The better clients will expand to show the whole back & forth of the conversation, if it exists.

haha, I used to wonder exactly the same thing. I asked my friend who actually uses Twitter, and he basically said, "You're doing it wrong." He said that Twitter is all about the stream, and using it for historical conversations like that is awkward and difficult. Which makes me question the point, but there you go.

I use the Seesmic web and Android client, mainly because they do a great job of showing conversations (click 'in reply to' in the meta message).

That does require that the comments are public (or that the author has granted you access to view the comments if private).

When you follow someone their updates appear on your home page and you never see @replies to other people.