GPS receivers are able to operate at signal level of -150 dbm or less, but mobile phones need far more than -115 dbm level signal. Why GPS receivers are so much more sensitive than GSM or WiFi receivers? See these receivers
There are a few factors at play.
Firstly as Olin indicated the signal bandwidth and data rates are different.
It is a fundamental rule of information theory that the maximum amount of data you can pass through a data channel depends upon the channel bandwidth and the signal to noise ratio. See the Shannon-Hartley theory for details.
This means that if you have a lower data rate or a wider channel you can cope with a higher signal to noise ratio.
The GPS navigation message sends data at 50 bits per second over a channel that is around 20MHz wide. WiFi 802.11n tries to get 72Mb/s or around 1 million times more data over a channel that is 20MHz wide.
This would indicate that GPS can cope with significantly lower signal levels than WiFi
But that only tells you what is theoretically possible, not how to achieve it.
A GPS signal is very predictable. Each satellite is broadcasting a pesudo random data sequence which repeats every millisecond, the data is then added on top of that every 20ms. The GPS reciever knows what this pattern is and looks for it in the background noise. It does this by making a guess at the timing of the signal and then moving this expected timing around until the correlation between the expected and recieved signals is maximised. By doing this the GPS reciever can effectivly find a signal that is weaker than the random background noise.
This has the added advantage that since the signal is random it looks like noise unless you are looking for it. This means that all the satellites can broadcast on the same frequency at the same time without interfering with each other.
Another advantage of this system is that the primary information of interest to a GPS reciever is the exact timing of the recieved signals. By maximising the correlation between the expected and actual signals you get a very robust and accurate way of determining the exact signal timing.