I'll try to be careful with my words here (to avoid ambiguity more than anything else), but there are different programmes in different countries that provide different degrees of interception.
In the UK we have the Regulation of Investigatory Powers Act 2000, which amongst other things forces service providers to keep logs of Internet activity for the police. These logs are typically of the order of IP address and connection type, not the actual data itself. This applies to pretty much all Internet access coming out of the UK somewhere along the line.
Beyond the police there are means of intercepting specific Internet traffic. It's easier for me to talk about US interception capabilities at that level though (as it's more publicised). The FBI, NSA, CIA and (if IIRC but they might be colluding with another agency) the DHS all have their own independent capabilities for broad sweeps and targeted surveillance. These capabilities are exercised according to remit. The agencies have information sharing agreements with each other, and the relevant agencies have international sharing agreements with their counterparts e.g. UKUSA intelligence sharing agreements etc.
If you want anonymity, you have to understand what you're trying to protect yourself from and (if possible) your adversary's capabilities. Having worked in countries with significant local interception capabilities that I do want to protect against, usually a properly configured VPN or SSH tunnel to a safe country is about as good as you're going to get without getting into government crypto (and if you're using government crypto in a hostile environment like that you're probably breaching some rule somewhere anyway).
As to the question of whether or not Tor is safe, I assumed it was public knowledge that various countries' intelligence services ran monitored exit nodes for quite a while. I've seen malicious Tor exit nodes in investigations and have known people who've set them up for the express purpose of monitoring them.
In the UK we have the Regulation of Investigatory Powers Act 2000, which amongst other things forces service providers to keep logs of Internet activity for the police. These logs are typically of the order of IP address and connection type, not the actual data itself. This applies to pretty much all Internet access coming out of the UK somewhere along the line.
Beyond the police there are means of intercepting specific Internet traffic. It's easier for me to talk about US interception capabilities at that level though (as it's more publicised). The FBI, NSA, CIA and (if IIRC but they might be colluding with another agency) the DHS all have their own independent capabilities for broad sweeps and targeted surveillance. These capabilities are exercised according to remit. The agencies have information sharing agreements with each other, and the relevant agencies have international sharing agreements with their counterparts e.g. UKUSA intelligence sharing agreements etc.
If you want anonymity, you have to understand what you're trying to protect yourself from and (if possible) your adversary's capabilities. Having worked in countries with significant local interception capabilities that I do want to protect against, usually a properly configured VPN or SSH tunnel to a safe country is about as good as you're going to get without getting into government crypto (and if you're using government crypto in a hostile environment like that you're probably breaching some rule somewhere anyway).
As to the question of whether or not Tor is safe, I assumed it was public knowledge that various countries' intelligence services ran monitored exit nodes for quite a while. I've seen malicious Tor exit nodes in investigations and have known people who've set them up for the express purpose of monitoring them.