Looking at a recent question, my thoughts turned to instruments which can be played left- or right-handed, without alteration. Given that approx. 85% of us are right-handed, it's hardly surprising that most instruments are appropriately made. However, bugle/trumpet/flugel seem to be ambidextrous,as are drums, but maybe not a kit of drums, which often gets set up opposite by a lefty drummer. Which other instruments could fit into this category. And - apart from one left-handed piano I heard about (!!!!) are there specific other instruments ?
TL;DR: With the notable exception of guitar, all classical instruments are taught "right-handed" regardless of handedness of the student, as there is no detriment past an intermediate level of instruction.
Now that I think of it, the only truly ambidextrous instruments might be the harmonica (since you can flip it upside down), slide whistle, handmade or otherwise invented instruments, or certain types of "found instrument" percussion.
Even instruments like the harp or piano have pedals to contend with that favor one side over the other, and all instruments with a keyboard layout are ordered low to high from left to right, which makes sense when you consider that bass lines are usually much less active than higher melody lines.
The vast majority of instruments, including all of the wind instruments and classical bowed string instruments, come in only one variety--and while that variety is biased towards right-handed people, they are learned by left-handed people all the time without alteration.
There are very few notable exceptions where instruments can be set up for left-handed people differently from right-handed people. Guitar and drum-set are the two that most readily come to mind, and I would attribute that to those instruments' sheer popularity and use in popular music, as contrasted with a more formal style of classical training used for other instruments.
Some specific examples addressing instruments referenced in previous answers that only come in one design:
- Snare Drum - music is written with L/R sticking
- Trombone - valve attachments can only be actuated by the left hand; teachers intend for the students to eventually graduate to instruments with a valve, so a reversed horn is never taught.
- Trumpet - 2nd valve slide and bell throat are designed so the instrument is held by the left hand
- Recorder - many soprano recorders come in one-piece varieties (without a separate bottom joint), and larger recorders only come in "right-handed" configuration, so, like the trombone, students will just be taught the standard configuration so they have more opportunities later
- Flute - even without keywork, they are typically designed with an important leading edge inside the tone hole that can only be blown across from one side with any success
- Theremin - In addition to the antennae designed ever-so-ergonomically to favor one side over the other, electronics controls are only located on one side of the instrument (ostensibly the one facing the player).
A trumpet is difficult to play lefty, as the tuning valve is placed to one side of the main valve set, and hard to reach from the far side.
Now, any flat-necked string instrument (e.g., guitar, erhu, banjo) can be played as-is lefty, tho' you have to rethink your methodology since the strings are effectively reversed.
The recorder, at least the upper (no keys) ones, can be played lefty with a little finger stretching and rotation of the bottom joint. As to piano-- I'm not sure what you define as "lefty," given that both hands are pretty busy, and there are known pieces w/ cross-hand action. The washtub bass (or any single-string instrument) is ambidextrous. I dunno how accordionists would feel about their line of instruments being included here.
Percussion instruments don't really count.
Here are some, in a wide sense, symetrical instruments:
- Harp (possibly except for the pedals)
- Trombone (without valve extensions)
- Harmonica (with exceptions such as the double decked bass harmonica)
- Digeridoo and similar non-keyed instruments
- Some flutes with straight finger holes
- One-chord instruments such as a traditional washtub bass
Tin whistle and their relative the low whistle are truly ambidextrous instruments.
There are some examples of the larger low whistles having their finger-holes offset from the centre line to make the reach slightly easier, but they aren't the norm.
I'm a lefty and have been playing the Chapman Stick for a year now. I really believe this is an ambidextrous instrument. Usually, you play the bass strings with your left hand and the melody strings with your right, but you can also use your right thumb to tap a bass string or your left thumb to tap a melody string. Or you can play uncrossed (left hand on melody, right hand on bass), or play a bass part with both hands, or a melody with both hands, or even some more interesting harmonic stuff, playing "split arpeggios" or "big fat chords" with both hands, by leveraging the overlap between bass and melody.
When I first wanted a Stick I thought about ordering it "lefty", that is with the strings inverted, but then I decided against it after thinking about it for a while, realizing it's a completely different instrument and I should learn it as such, instead of wanting to "map" it as a bass+guitar or a piano.