Ground Faulc Circuit Interruptors.

About

Is GFCI safer than a ground pin? Yes, in case a part of an appliance is not grounded. How a ground works - [1]. Also - just because there is a ground pin - it doesn't mean that it is connected or that it is connected properly.
Grounding without GFCI provides personal safety, safety for electronic gear, and fire safety. GFCI without grounding provides better personal safety than grounding, fire safety, but no safety at all for electronic gear. - [2]
Is it possible to both ground and use a GFCI? Apparently yes - second paragraph of top answer. [3]
According to NEC 2014, you are not allowed to ground a GFCI [4] -

Note that voltage surges are yet another thing - and a GFCI does not protect against those. Use a surge protector - [5]
GFCI is required by code for outdoor receptacles - [6], and for construction sites.
Ground fault protection protects heavy industrial equipment. Beyond the scope of GFCI discussion. [7]
Case where GFI does not work - is that dangerous when? [8]

More

Can be wall outlets. $9.
GFCI circuit breakers also exist, but are expensive at $40 each - [9]. $30 on Ebay - [10]
DIN Rail GFCI breaker - $5 - [11] - is this really GFCI?
Can be plug-in receptacles - [12]
Arc Fault Circuit Interruptors (AFCI) are another thing - [13]
Note that GFCI outlets sense differential current, and they are not grounded - [14]
Portable GFCI - GFCI on a power cord - [15]
A GFCI outlet is quite complex - with its own circuitry. See teardown and explanation - [16]
GFCI chip from On Semi - [17]