LGA 775 = Pentium 4/D & Core 2 series of processors. Most motherboards with this socket use DDR2 memory, some use DDR3, and this memory is run in dual channel. Advantage is that cheap builds which perform quite well can be made like Pentium Dual Core E5000 series. Disadvantage is that it is quite old, and the newer CPUs are faster with more features and better power consumption, and no more new CPUs will be made for this socket.
LGA 1156 = Pentium G6950, Core i3, Core i5 & Core i7 800 series of processors. Motherboards with this socket use DDR3 dual channel memory. This is Intel's mainstream platform and can perform well, sometimes faster than their LGA 1366 platform for a bit less - many different processors and motherboards are available. Disadvantage is that with LGA 1156, you are stuck with the P55/H55/H57/Q57 chipsets which only offer one x16 lane, or two x8 lanes, making implementation of SATA III and USB 3.0 quite difficult, and is less futureproofed for higher end cards.
LGA 1366 = Core i7 900 series of processors. Motherboards use triple channel DDR3 memory, and this is Intel's enthusiast platform. Comes with two PCI-E x16 lanes and offers full bandwidth when graphics cards are used in CrossFireX or SLI with the X58 chipset. This is the most expensive platform of all however, and X58 boards are more expensive than their P55 chipset cousins which have similar features. Only supports the Core i7 900 series of processors.
Note that none of these sockets will support Intel's Sandy Bridge based processors.