There might be a program out there that allows you to get Twitter updates without getting a Twitter account (I am however not aware of it). But I see no reason not to get one. It's completely harmless. There are hundreds, if not thousands, if not tens of thousands of folks on Twitter that are there simply to receive tweets and not send them.
And yes, you can set it up so that the people you follow when they tweet, it can be sent to your phone or some other device as text messages.
The "normal" way you check is just by going to twitter.com, signing in with your account name, and on your homepage it will show all of the latest tweets from the folks you follow.
There are also programs that you can download to your phone/other device/computer that does all the work for you of checking updates and stuff. Popular ones include TweetDeck (which is what I use), Echofon, UberTwitter, among others. As far as I'm aware, almost all are free.
And if/when you decide to join, be sure to follow falcfans