Learning the principles of op-amps - Why are there so many?
There are so many different amplifiers because there are so many different applications, each requiring different attributes.
A perfect voltage amplifier, for example, has infinite input impedance and zero output impedance. Neither of these exist in a real amplifier, of course, but there are devices with Gigohms of input resistance (look for a JFET input stage device, for example).
A perfect differential amplifier (within which opamps exist) has zero offset between the inputs, but once more, no such device exists. This Vos term is always stated in datasheets. In a high gain situation this input offset appears as an output offset voltage given by Vos * gain. Where tiny signals must be amplified (as in a strain gauge for instance - there are numerous applications here) we would use what is known as an Instrumentation Amplifier which is a device optimised for high gain, low offsets and high CMRR amongst other things.
Perhaps you are in a battery operated system and need a low quiescent power amplifier. The trade-off here is usually Gain Bandwidth Product although advances are still being made in this area (as it is in all areas, but with the Internet of things appearing, this is becoming a key driver).
Perhaps you need a really fast Video Amplifier for clean amplification of video signals.
There are High Speed amplifiers, optimised for GBW. Then there are Zero Drift amplifiers.
By now, you may be getting the idea that so many different types of device exist for the very good reason that each type has been optimised for a particular task: which one I choose depends on the specific requirements of the application.
I have barely scratched the surface here, but I suggest looking through the tables for these devices at Linear Technology, Analog Devices and Texas Instruments for starters. Maxim Integrated also has an excellent series of tutorials ans application notes.
All these manufacturers have excellent tutorials and application guides that are a wonderful resource for anyone wishing to learn about these devices.
As noted by Adam Haun, there are amplifiers that are designed to have a minimum gain well above unity; the advantage here is better transient response as the Dominant Pole (scroll down in page) can be at a higher frequency, maintaining more bandwidth at lower frequencies. These devices are not unity-gain stable, and therefore may not be used at lower gains.
Edit. Added current feedback amp: Thanks for the reminder, LvW
A typical current feedback amplifier has incredible slew rate. This one is listed at 1600V/us which while available in many devices, is still truly astounding in an 'ordinary' amplifier. Although these devices can be a little more difficult to understand at first, they have significant advantages when used appropriately. Read this application note for a good example.
Another update
As can be seen from the comments, amplifiers come in many different flavours, such as differing output drive current, rail to rail outputs (many can only go to within 1.5V of the power rails), rail to rail inputs (usually requires a dual input stage which can have its own very peculiar effects), yet others optimised for high side sensing (the common mode range can exceed the power rail) to name but some possibilities.
There are others designed for ADC interfacing that can have an external common mode reference so that the output is always centred in the middle of the ADC range, truly fully differential devices and more.
The range of amplifiers available is truly enormous. What was a 'general purpose' amplifier 20 years ago is now 'low end' although as noted many older amplifiers are still available, for a number of reasons.
The key to choosing an amplifier is deciding which features of the perfect op-amp you need to most closely get.
One way to become familiar with amplifiers without actually making the circuit (at first) is to use a simulator. There are a number of these around, such as LTSpice and there is a free version of Simetrix (node limited) amongst others.
When using simulators, you will need to understand the limitations of the models used. There is an excellent application note at Linear Technology that shows what the models really contain (and it is not the actual circuit in the amplifier).
HTH
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JUST ALWAYS USE TL071
:)
Or maybe LM741.
Too many devices? The situation is similar with all components. Have you seen the number of 1K resistor types you can buy on digikey?
OK, what should we use as a general-purpose hobbyist op amp? For beginners, the Op-Amp rule used to be simple: always use Fairchild uA709 op amp for everything, later becoming uA741, then later the Texas Instruments LM741. That was the 1970s hobby era of the 555 timer and 741 op amp, or maybe quad LM324. No thinking needed, just plop in a 741.
Perhaps twenty years later the rule had become: TL071 op amp for everything, or TL072 dual version. These were very similar to LM741 but wider bandwidth, low noise for use with high gain circuits or audiophile pre-amps, with lower power for long battery life, and had JFET-input for extreme high input impedance. These are still in heavy hobbyist use today, although getting a bit 'classic.' 'Vintage.' Yet most textbooks still go deeply into LM741, and ignore anything later.
Or sometimes we'd use CA3140, with MOSFET input for weird stuff like ion counter or picoamp detectors or Giga-ohmmeters or touch sensors. And if you needed your output to go all the way to power supply rails, get LMC6082 rail-to-rail op amp or maybe OP162 (but those only could use +-7V supply, not +- 9V, or twelve or fifteen.)
Back in those days the workhorse for industry was the fairly expensive OP-07 laser-trimmed op amp from Analog Devices. No "zero-ing trim pot" needed; already been factory-adjusted WITH LAZARS. The pros had the OP-07, and the hobbyists had 741. The OP-07 was the one used in old Horowitz-Hill chapter seven. Today you might instead use an OPA27 in the same application. Or go fast and loose with OPA37G.
As for beginners today ...I dunno. Stock your little plastic drawers with LM741CN, TL071CP, LMC6482IN, OP27GP, then go from there. Search out the schematic-archive hobby-project sites and see which op amp they have in each particular schematic. But instead, if you're going full-on custom design, and need 30MHz or 900MHz bandwidth, or ultra-extra-hyper-low supply current, or 2.5V supply voltage, then trudge through mouser or digikey parts search page.
And maybe go on eBay for some Fairchild uA709 or uA702 as collectible antiques?
PS. Note that Murphy's Law declares that the perfect op amp for your project will end up being sold ONLY as surface mount smt versions, no DIP package made any more. Cannot plug into white protoboard blocks. But you can now buy a $5 "SOCKET ADAPTER SOIC TO 8DIP," little Surfboard thingies with eight pins, to let you solder it on, then plug it into your proto board. If five bucks for a DIP modification socket is too steep, just remember, always use TL071 for everything.
PPS. Actually answering the OP question? Yep, one big reason for bazillion op amps is the competing manufacturers all having their own separate products for a single niche: Fairchild and Burr Brown and Texas Inst. and Analog Devices and National and RCA and Motorola and Exar and Intersil and Maxim and Micrel and Lin Tech. If they all just sold a single 741-lookalike, still there'd be twelve different kinds! ( Some of those went out of biz or merger-d with others, while new ones popped up.) Then, each one has their low-noise version, their FET-input version, their all-CMOS version, their "precision" trimmed offset version, single supply versions going below 5V, 3.3V, 2.5V, 1.7V. Also single op amps and dual op amps and quad op amps. Zero-drift chopper-stablized versions. And redesigned highspeed versions going up to 1.3MHz, to 1.5, 2, 3, 4, 8, 10, 30, 64MHz. And specialized "high slew rate" versions, not necessarily the same as the wideband ones. You can get "instrumentation" versions with on-board resistors and programmable gain. And versions with a "shutdown" pin for battery operation and zero-power sleep mode. Then besides normal op amps there's the "Norton" amps with current input, and ultra-speed CFA "current feedback" 900MHz op amps, ten-watt power op amps in TO-3 cans, five kilovolt op amps for field-electrodes or piezo drive, etc.
At least the part numbers usually stay about the same for all ?thirty? different surface-mount package types.
The thing that's usually special about each op-amp is how well they approximate (or don't) the ideal op-amp. In theory if you stick within their specifications the ideal op-amp model works. Don't worry too much, though. If you're doing something which is a few kilohertz and doesn't need to be too accurate (say, less than 1%) pretty much any op-amp will work.
A few op-amp like devices are often grouped with op-amps on some websites, though their function is different from how the traditional ideal op-amp works. Examples are "buffers", "instrumentation amplifiers", and "differential amplifiers". These may sound familiar if you've studied op-amp circuits because they often encapsulate the behavior of op-amp circuits into a single chip. They're great for building larger circuits which use these components because they're optimized for that specific application, but aren't so great for figuring out how their guts work.
The last major difference is what package the op-amp comes in. Some are very tiny and have to be surface mount soldered. Others have pins you can plug into a breadboard. Functionally they may be the same, but for prototyping and playing it's much easier to just plug it into a breadboard than have to design a custom PCB and solder the chip in.
Without knowing more about what you want to test, I would recommend looking for something marketed as a "general purpose" op-amp in a DIP form factor (dual in-line package). These have physical pins which can plug into a breadboard and generally offer average performance across the board. For example, the LM324 is one of these jellybean op-amps. It also happens to come with 4 op-amps in a single chip, so you can build more complicated circuits without taking up as much space on your breadboard (or just ignore them if you don't need them).