The only sure way to obfuscate your IP address is to use an IP address that isn't registered to you.
They sure tracked this guy down pretty quick when he used Tor
http://www.theverge.com/2013/12/18/5224130/fbi-agents-tracked-harvard-bomb-threats-across-tor
Actually it is probably not always useless. Unlike a VPN which is a single proxy server, Tor (and other Chaum mix-nets such as I2P) employs onions layers of hops over multiple servers (for Tor I think it is normally 3 unless both are Tor services then 5), so if any one of the servers is not compromised then the obfuscation of your IP address may be achieved. However, don't forget the other possible attacks such as timing analysis by a global adversary even to servers in the onion layers it has not compromised or control, end-to-end attacks such as the use of the Harvard wireless network in the above linked story, and the browser attacks (and other spyware).
If you are using an unregistered connection as I suggested above, then you may already be suspicious to the NSA, thus adding Tor (Tor Bundle or Whonix) may provide another layer of potential imperfect anonymity. The more layers the better if you were already going to be suspicious and not hiding in plain sight due to your use of an unregistered internet connection. For example, lets assume the following probabilities which I pulled out of my ass:
1. 20% chance the surveillance can track your unregistered mobile IP and correlate it to your identity.
2. 20% chance a Tor session's anonymity fails
3. 50% chance a VPN is compromised (or has insufficient users to mix with)
Using all 3 layers together means your probability of not being anonymous decreases to 0.2 x 0.2 x 0.5 = 0.02 = 2%.
However, lets say you are not using a suspicious connection to the internet and lets assume the NSA doesn't save all traffic (only filters and saves suspicious and all encrypted traffic), then using Tor may be detrimental as your probability of be recorded goes from very small up to say 20% (if the #2 is a correct guesstimate).
Let us analyze the probability factors for #1.
Try to never use your unregistered mobile connection from or too near to your residence as triangulation is real.
Also your phone likely has GPS in it which can perhaps be activated remotely by the NSA as well.
Also your late model car may have a GPS in it that is potentially reporting to the provider as admitted last year by the Ford CEO.
Also there are often cameras along the way on stop lights, sides of buildings, etc..
Also your mobile device may be reporting to WiFi hotspots all along the path of your travel.
Also the triangulation and position tracking data of your mobile is probably archived by the providers.
If you are a person who the NSA is determined to identify, it is very difficult because there are video cameras hiding every where, except maybe not in the forest or desert, but satellites (or unmanned drones) can read the VIN number on your dashboard and your license plate, and they could pull up all this archived data after the fact. Apparently there is even infrared technology so they can see through the clouds and at night. The surveillance technologies will continue to improve.
Thus:
1. Never use that mobile for any activity that can be correlated to your identity, i.e. use it very sparingly only for the one anonymous activity of importance.
2. Remove the battery and the simcard from the mobile device when not in use. I say remove both, just in case there is some capacitor some other undocumented means of powering the device to give a homing signal.
3. Either travel to some remote, lonely place in some way that your vehicle and yourself can't be identified by any of the above pitfalls, or travel even if identified to a very crowded location wherein the known location of your mobile can't pinpoint who in that crowd is holding the mobile which is sending the data. So in the latter case, you would want to make sure you can't be seen on an video or satellite imagery in a way that could identify you as the one in the crowd operating a laptop-- much better you accessed the internet from the mobile device touchscreen instead of attaching it as modem to a laptop (so you don't stand out in the crowd). And note that the accuracy of triangulation and or GPS is getting near to a meter or meters, so it would need to be a very crowded place such as train station, mall, bar, disco, sporting event, etc.. The problem with the hiding in a crowd approach is that eventually it can be correlated that your face always appears in the crowds, you stay in one place too long, or your movements on video correlate with the tracking movements of the mobile, so this isn't really going to work if more than once or for two long of a period of time. Thus realistically you need to travel and use the unregistered mobile device in a way that you can't be identified in any surveillance. This is difficult to accomplish. Even older model cars can still be tracked by their license plates. And most public transportation has surveillance video.
Even if you traveled by bicycle or by foot, you can be identified from your originating location (who enters the location and who doesn't emerge is a process of elimination, e.g. a parking garage) and tracked along the way in archived surveillance (remember archived video that captured 9/11 attack on the Pentagon).
You will need to be very clever. If the activity you are doing is not immediately suspicious and would only be investigated weeks or months hence, perhaps you can hope that non-government (privately) operated video surveillance archives will be discarded after some time, but I wouldn't really be so confident about this.
Why do you think they made this phoney terrorism so that can put surveillance at every crowded event.
Also most of you have already identified yourself as being one of the 0.001% who is interested in anonymity. Thus if you are identified in a crowd, you will automatically be a prime suspect.