Let's say you want to follow someone on Twitter without letting them know. Maybe it's a competitor, and you're interested in what they have to say, but maybe they don't yet know you're competing with them. How can you follow them without broadcasting your interest? If they're protecting their tweets, you can't. But in most cases, it's easy. All you need is social media's universal solvent: RSS.
If you want to be stealthy, you can't just click follow, because that sends a notification to the person you're following. Not stealthy. Instead, load up the Twitter page of the person you want to track, and look for the link to the RSS feed at the bottom. Subscribe to the feed, and you'll see the person's tweets without notifying them.
Update: RSS feeds no longer appear on individual profile pages, but you can still use RSS to follow people with Twitter's advanced search. The feed URL looks like this:
Seeing both sides
If you want to see the other side of your target's conversations, set up a search feed on Tweet Scan. Search for the target's handle in the first box to see public responses to that user, and then subscribe to the feed for that search. (It's not a bad idea to subscribe to that search on your own account, in case you miss an @ reply.)
Using RSS like this means you lose some of the communications benefits of following and being followed, and it's not really in keeping with the community vibe on Twitter. In most cases, it's better to follow the people who interest you and be a part of the community. But if want to see what someone says without announcing your presence, or if you really don't want to use a separate client for monitoring Twitter, RSS does the trick.
If you tolerate the lower signal:noise of Twitter and want to follow me, I'm @gilliatt. Original, I know.