LiveJournal has never allowed any real web analytics to be added to personal journals, although sponsored communities were able to get them. Sure, you could add stat counters or web bugs from LJ Toys. But I'm unaware of any way on LiveJournal to get the referral URL of people who were linking to your post, save for the recently implemented and entirely optional pingbacks.
Dreamwidth, however, is going to give paid users Google Analytics as a feature. This means that paid users will be able to know who in DW is linking to them, leading to some interesting changes from the way things used to be. I think this has the potential to surprise and upset people.
For instance, let's say you link to someone's post in a friends only post in your journal or use <user name="user"> to link to their journal in a locked post. Some of your access given subscribers click on that link, and if the user you linked to is paid and using Google Analytics, they'll know you were talking about them in a post they don't have access to, and if you linked to a specific post, they'll know which post you're talking about. Stealth talking about people has become that much harder and unreliable.
There's a limited ability to avoid this. URLs are automatically turned into links; you can do formatting to make it unlinked, so people have to copy and paste, but some people have browser extensions that will autolink anything that looks close to a URL, so you can't always depend on that. You'll have to go above and beyond to obfuscate the link to make sure that doesn't happen and not use user tags to link to someone--but if you don't do that, someone is bound to make a Greasemonkey script that could go to a highlighted name, and they'll still get the referral.
Edit:
charmian and
kaki point out that URL obfuscators might get used more, like TinyURL and anonym.to. I agree with this! However, there are even browse add ons that resolve those services to their actual URLs, so even that is not a failsafe.
What effects do you think this is going to have on social interactions on Dreamwidth? What other effects will Google Analytics have on users?