I\'m super excited about my program powering a little seven-segment display, but when I show it off to people not in the field, they always say \"well what can you do with it?\"
First: They don't need to have volatile memory.
Indeed the big players (Xilinx, Altera) usually have their configuration on-chip in SRAM, so you need additional EEPROM/Flash/WhatEver(TM) to store it outside.
But there are others, e.g. Actel is one big player that come to mind, that has non-volatile configuration storage on their FPGAs (btw. this has also other advantages, as SRAM is usually not very radiation tolerant, and you have to require special measurements when you go into orbit).
There are two big things that justify FPGAS:
Price - They are not cheap. But sometimes you can't do something in software, and you need hardware for it. And when you are below a certain point in your required volume (e.g. because its just small series, or a prototype) an FPGA is MUCH cheaper than an ASIC. Also, while developing ASICs this allows - before a final state is reached - much higher turn-around times.
Reconfiguration - You can reconfigure your FPGA. That is something a processor or an ASIC can't do. There are some applications where you can use this: E.g. When you need the ability to fix something in the design, but you can't get physically to the device. Example for this: The mars orbiters/rovers used Xilinx FPGAs. When someone finds there a mistake (or wants to switch to a different coding for transmitting data or whatever), you can't replace the ship, as it is just not reachable. But with an FPGA you can just reconfigure and can apply your changes. Another scenario is, that you can have one single chip which is able to perform different accelerations, depending on the scenario. Imagine a smartphone, when telephoning the FPGA can be configured to make audio en-/decoding, when surfing it can work as a compression engine, when playing videos it can be configured as h264 decoder/accelerator. Another thing you could do is that you can match your hardware to your problem instance. E.g. Cisco uses many FPGAs in their hardware. You need the hardware to perform switching/routing/packet inspection with the required speed, and you can generate from actual setting matching engines directly into hardware.
Another thing which might come up soon (I know some car manufacturer thought about it), is for devices which include a lot of different electronics and have a big supply chain. It's more or less a combination of price and reconfiguration. It's more expensive to have 10 ASICs than 10 FPGAs - where both perform the same task, but it's cheaper to have 10 FPGAs with just one supplier and the need to hold just 1 type of chip at service and supply than to have 10 suppliers with the necessity to hold and manage 10 different chips in supply and service.
True story.
They allow you to fix design flaws in the custom data-acquisition boards for a multi-million dollar particle physics experiment that become obvious only after you have everything installed and are doing integration work and detector characterization.
FPGA are also used to test/research circuit design before they start mass production. This is happening in several sectors: image processing, signal processing, etc.
Edit - after few years we can now see more practical applications including finance and machine earning:
I like this article: http://www.hpcwire.com/hpcwire/2011-07-13/jp_morgan_buys_into_fpga_supercomputing.html
My feeling is that FPGA's can sit directly in your streaming data at the point where it enters your the systems under your control. You can then crunch that data without going through the steps a GPGPU would require (bringing the data in off the network, passing it across the PCI Express bus and crunching it a Gb at a time).
There are good reasons for both, but I think the notion of whether you mind buffering the data is a good bellwether.
Here's another cool FPGA application:
https://ehsm.eu/m-labs.hk/m1.html
You can evolve circuits, this is a bit old school evolutionary algorithms but starting from a set of random individuals you can select the circuits that score higher in a fitness function than the rest and breed them to create a new population ad infinitum. read up about Evolutionary Hardware, think this book covers FPGA's http://www.amazon.co.uk/Introduction-Evolvable-Hardware-Self-Adaptive-Computational/dp/0471719773/ref=sr_1_1?ie=UTF8&qid=1316308403&sr=8-1
Say for example you wanted a DSP circuit, you have an input signal and a desired output signal, starting with a random population you select perhaps only the fittest (bad) or perhaps a mixture of fitties and odd ones to create the next generation. after a number of generations you can open the lid and discover low and behold evolution has taken place and you have a circuit that may even out perform your initial expectations!
also read the field guide to genetic programming, it's free on the web somewhere.
Automotive image processing is one interesting domain:
Providing lane-keeping support to the driver (disclosure: I wrote this page!):
http://www.conekt.co.uk/capabilities/50-fpga-for-ldw
Providing an aerial view of a car from 4 fisheye-lens cameras (with video):
http://www.logicbricks.com/Solutions/Surround-View-DA-System/Xylon-Test-Vehicle.aspx