None of these answers are actually answering the question, and nobody is mentioning the power behind meta data. Let's go into detail as to how this can be done.
How can you be caught using Private VPN when there's no logs about who you are?
Generally speaking, there are logs about who you are, even if your VPN provider isn't logging anything about your connections. Other companies are logging other information about you. Advertisers, etc.
While a VPN provider may claim not to provide connection logs, their internet service provider may do it. They may be telling you the truth, but not the whole truth.
But to answer your question, let's approach this subject from the assumption that your VPN provider is not logging anything.
Metadata is far more powerful than most people realize
Meta data is powerful. When metadata can match you to other data sources, finding you is not difficult.
I created a very dumbed-down flowchart to help explain how this can happen. Sure, different operating systems make this harder, but in general, it's much easier to find a Mac or Windows user, or a mobile device user than it is a Linux user.
Before you read, assume Device ID could be anything: your windows key, your hardware device information communicated to providers, your MAC addresses used, IP addresses, browser fingerprints, whatever. It could be any number of things.
What kind of account information could assist in giving you away?
Any service you use online for which you log into an account for. These include, but are not limited to:
- Email accounts
- Xbox Live
- Discussion forums
- Windows update
If you connect to any of those while connected to a VPN -- and many of these are automatic connections that re-establish themselves once you connect to the VPN -- a clear pattern has arisen.
And that's just a tiny list. There's a countless number of services which will do the same thing. And those service providers will log your access attempt, and are required by law in most countries to turn over that data if requested.
In most cases, you can run... but you can't hide. :) Sure, there are ways around this, but the vast majority of VPN users aren't really aware of this. This is one of the many reasons how those "hiding behind 7 proxies" keep getting caught.