Wait, is it musicology Tuesday already?

The ancient Greeks played the aulos. Also see the salphinx and the kithara.

The harpsichord was one of the two great keyboard instruments of the Renaissance and the baroque. It was replaced by the piano, but it has been luckily brought back to life! It is back again with us and is no longer considered too rare, but many people are not familiar with it.

The clavichord was another popular instrument. MUCH smaller, quieter and cheaper than harpsichords. It was not meant for big public performances, people would play it in more intimate settings, or use it to practice.

The lute. Not particularly rare... However, the theorbo will get more people looking.

The viola da gamba had a lovely sound. It's close to a cello, but it has frets.

The cornetto was just lovely. It works like brass instruments, but it's made of wood and has holes like a flute. Fantastic little instrument...

The dulcimer (played by the lady in black who is standing in the middle).

The hurdy gurdy. With that name, it has to be weird...

The crumhorn. Related to the oboe (double reed) but it has a cap, so the player is not in direct contact with the reeds. Not to be confused with the hirtenschalmei.

The rackett.

There were more peculiar medieval instruments, some look less alien and closer to modern ones.

The arpeggione had a few years of fame in the 19th century.

Some of the instruments I mentioned probably were not as popular as the guitar is today. It is very easy to find instruments that are still used but look completely weird outside of the Western world. Many instruments are in principle related to others, and you can find variants of many things that are normal (they just look strange to us). Middle Eastern instruments related to medieval instruments (that are now dead), for example.

Mechanical instruments were popular at some point. For example, nickelodeons.

We don't have to go far into the past to find weird instruments that are not really part of contemporary music. For example, stylophones (the little thing operated with a stylus). At some point, people were studying theremin just like others were playing the cello. People had great hopes for the future.

The study of musical instruments is called organology. People who are into that know about the craziest instruments (and many are still used today).

The accordion.

Any way you want to slice it, from number of countries in which it figured prominently, to percentage of traditional musical traditions that absorbed and incorporated it, to sheer number of people who played it, the accordion ruled for a good chunk of the 19th/early 20th century.

It could be produced in bulk through modern factory methods, learnt by Joe Public through systemic charts and symbols, leant itself to the boom-chuck underpinnings of the popular dances of the day, didn't fall apart under rough conditions, was loud enough to drive a room without amplification, and could be played while singing or even dancing.

It figures in every tradition you know besides classical and post-19teens pop/social music. In your mind's eye try to see someone from each of these spots holding a squeezebox while people party:

Poland. Russia. Mexico. Texas. Louisiana. Italy. China. Germany. France. South Africa.

Can you do it? Bet you can. There's plenty more.

Actually, I may not have answered OP's question, since he did specify "fallen into obscurity" -- and in the eyes of much of the rest of the world, it hasn't.

But OP and most of the current pop media probably don't think of it as popular, so perhaps it still counts.

I know this isn't the traditional "instrument" that you're thinking of, but the original methods of writing music for tape as a form of musique concrete are long since archaic and mostly extinct. Back in the 1930s-50s, methods of recording via tape had become more commonplace, and as a result, many composers questioned/pushed the boundaries between live music and recorded music, often blending the two. Composers like Edgard Varèse would take field recordings e.g. recordings of everyday atmosphere and scenery, and cut and splice the tape together in such a way that it was no longer distinguishable. Combine that with the post-war existentialist philosophy of "what isn't music?" and you have some very interesting music that combines live performance with recorded sounds. Two examples that come off the top of my head are "Deserts", for tape and large ensemble, and "Poeme electronique" for tape (a prime example of splicing and cutting to get bizarre results). Nowadays, if something is written for live instrumentation + tape, it's usually prerecorded on a CD that someone in the sound booth or on the stage can just press play and go.

The most modern example I can think of this is an album that Jack White did not too long ago with this method, although I can't be bothered to remember the name of it as of right now.

Sources/further reading:

http://www.music.columbia.edu/masterpieces/notes/varese/notes.html

http://www.ipsden.u-net.com/course/EM3.html

Wright, Simms: Music in Western Civilization (media update), chapter 77

http://discorgy.wordpress.com/2008/08/04/varese-xenakis-le-corbusier-poeme-electronique-1958/

The ophicleide was a keyed brass instrument invented in the early 19th century as an improvement over the earlier serpent. (The name ophicleide means "keyed serpent".) It was replaced by the tuba in modern orchestras. Take a listen for yourself.