Well, there's a downside in the sense that no-one will ever see how you use web sites, so when they change their behaviour and break functionality you used to use, you'll have no-one but yourself to blame.
What other argument can there possibly be? The benefits to the individual aren't huge. And you're welcome to block GA, I'm just trying to make the point that there is a purpose behind analytics, and it isn't just a sinister conspiracy to take over your life.
I'm sympathetic to the purpose -- I'm less protective of privacy than most here.
My objection is to the means, namely, giving the page's author essentially unlimited access to compute resources on the browser and hoping the author will choose to be moderate.
Until 2008 I browsed the web on a slow machine (Celeron based on a PIII core, probably made in 2000 since the BIOS copyright notice referred to the year 2000) and blocking GA on that machine very drastically reduced the amount of time the browser was unresponsive. So much so as to suggest that even on modern fast hardware, there will probably be some improvement in responsiveness even if the difference will not be immediately noticeable to the user like it was on my old machine.
I don't like google and/or facebook having their tentacles reach out on far more websites than their own. I'm against centralized data gathering, even if it's futile in this world..
If you live in the EU, Facebook are not allowed to use the data gathered from their like buttons for advertising purposes, by order of the Irish Data Protection Commissioner.
Google Analytics is like loyalty cards for the web: they track user behaviour for the benefit of the service provider, not the consumer. But a "real" loyalty card at least pretends to serve the user by offering an occasional special deal or some savings, as opposed to added cost (bandwidth, load times etc). I vote with Ghostery.