It seems after some discussion that you are looking for a buffer amplifier.
Digikey has a section for this. if you go to the main area for linear amplifiers and then select for buffer type and in stock you get quite a list. I selected for those with an input current of 2nA typical I got a relatively short list(like 10). This however does not give me an easy way to share the links, so you will have to click it yourself.
These are designed to give you the features you want and in a small package, now they normally come in groups of 2^n, so you will have to get a package of 8, but I am sure you can make it work.
Markrages had a bit of extra input to add in a comment:
Cautions about those buffer amps: Most of them are made for video signals and so they are high bandwidth / high current designs. That's a consideration if the circuit is battery powered. Also note that (the ones I looked at) are specialized, single vendor parts. More expensive and more availability risk than op-amps or transistors with standardized footprints. Engineers have a duty to only use oddball parts when their special features are necessary and relevant to the design.
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.
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).
Op amps are pretty close to being ideal differential amplifiers. So the real question is, what's so great about amplifiers? There are (at least!) three answers.
First, the obvious -- amplifiers let you change the amplitude of a signal. If you have a small signal (say, from a transducer), an amplifier lets you raise its voltage to a useful level. Amplifiers can also reduce the amplitude of a signal, which could be useful to fit it into the range of an ADC, for example.
Amplifiers can also buffer a signal. They present a high impedance on the input side and a low impedance on the output side. This allows a weak source signal to be delivered to a heavy load.
Finally, negative feedback allows amplifiers to filter a signal. So-called active filters (which use amplifiers) are much more flexible and powerful than passive filters (which use only resistors, capacitors, and inductors). I should also mention oscillators, which are made using amplifiers with filtered positive feedback.
Amplitude control, buffering, and filtering are three of the most common things you can do to analog signals. More generally, amplifiers can be used to implement many kinds of transfer functions, which are the basic mathematical descriptions of signal processing tasks. Thus, amplifiers are all over the place.
Why op amps in particular? As I said, op amps are essentially high-quality amplifiers. Their key characteristics are:
These characteristics mean that the behavior of the amplifier is almost entirely determined by the feedback circuit. Feedback is done with passive components like resistors, which are much better-behaved than transistors. Try simulating a simple common emitter amplifier across voltage and temperature -- it's not great.
With modern improvements in integrated circuits, op amps are cheap, high-performance, and readily available. Unless you need extreme performance (high power, very high frequency) there's not much reason to go with discrete transistor amplifiers anymore.