In the wider blogging world things aren't as simple as livejournal. Blogs tend to be organised on a vaguely adhoc basis, and hence there's no simple way to implement something like a friends page.
Most people who follow many blogs use something called a "feed aggregator" to pull together the various blogs. An aggregator might be a piece of software like a news reader or mail client (Thunderbird is a good example of this class) or it might be a website much like a livejournal friends page. Or it could be something quite different.
An aggregator works by pulling together a number of feeds. Feeds are distributed my the means of special files that contain the whole or some subset of the recent entries from a source (in this case a blog, but it could be a newspaper or other regular information source). The three most common formats for these files are called RSS and Atom&lowast. An RSS file looks something like this:
<?xml version='1.0' encoding='utf-8' ?> <!-- If you are running a bot please visit this polic <channel> <title>Squaring the circle...</title> <link>http://www.livejournal.com/users/senji/</link> <description>Squaring the circle... - LiveJournal.co <lastBuildDate>Tue, 01 Feb 2005 11:40:17 GMT</lastBu <generator>LiveJournal / LiveJournal.com</generator> <item> <guid isPermaLink='true'>http://www.livejournal.com/ <pubDate>Tue, 01 Feb 2005 11:40:17 GMT</pubDate> <title>What I did on my weekend</title> <link>http://www.livejournal.com/users/senji/199557. <description>A busy weekend probably deserves an lj <comments>http://www.livejournal.com/users/senji/199 </item>
(I've cut that widthways to avoid awkward long lines)
What the aggregator does is that it polls the feed files to see if there is anything new, and when there is it displays it. LJ itself can be used as an aggregator for RSS and Atom feeds (but new feeds can only be added by Paid Users). LJ also produces RSS feeds for its users.
Now, so the problem here is that the location of the feed files isn't consistent between sites, so in practice when you want to add a blog to your aggregator you have to find the location of the feed from the website (there is usually a little RSS logo, and it is possible to embed the location of the feed into the webpage <head> section, but not all browsers make it easy to get at this information) and then cut and paste this into your aggregator (which will often be another webpage elsewhere).
This is where SubscribeMe comes in. It isn't much help if you use a non-web based aggregator (although with a little client-side support this might be fixable). It has a list of the major Web based aggregators (and Aquarion is willing to add more). The first time you click on a SubscribeMe link it will offer you a choice of which aggregator you use and a tickybox. If you tick the tickybox it will store your answer in a cookie and so on subsequent uses of SubscribeMe (from the same computer) it will remember it. Once you have selected the appropriate aggregator then it will issue a HTTP redirect to the appropriate URL to subscribe that feed in your aggregator.
Thus, once you've set SubscribeMe up you have a one-click solution for subscribing to blogs (and other feeds) that support it. (If you're using LJ then it's a little more as it puts you in the "subscribe this user? which filters?" page).
∗ The confusing thing here is that there are two only vaguely compatible standards called RSS1 and RSS2 produced by different people...