Please let me know if you find any errors, or if you know of a link that should be included!
The short answer is: not really. I can make a wild guess, but don't hold me to it...
The value of an accordion depends on a number of things:ballpark figures. Then you've got two options, of course: sell or learn to play. Hopefully you decide for the second option!
The condition of the accordionFor second hand accordions, playability is valued higher than antiquity. Antiquity value would only start to kick in if it is _very old_, i.e. from the first half of the previous century; an accordion from 1829 by Cyrill Demian (that's the year it was invented, or patented at least) would be worth quite a bit even if it was completely unplayable, but even for an instrument from around 1900 you couldn't count on that (unless it is a really nice mantle piece, of course). If the accordion is not in a good condition, one should probably deduct the cost of the necessary repairs from the value of the accordion. If the bellows seem to be mouldy, that might be costly: In that case the reeds might be rusty and need replacement! To estimate how bad or how good it still is, have a look at an article about How to check out the condition of an accordion or Advice on Buying Used Squeezeboxes.
By itself the age doesn't matter, but for one thing: accordions have become better over the years. But apart from maintenance and retuning, accordions can easily last 20 years.
The brandOf course, apart from the condition, the value also depends on the brand. There must be hundreds. Roughly speaking, Chinese and East-European accordions (Hero, Parrot, Delicia, Weltmeister/Bandmaster) are of lower quality and cheaper than German, Austrian or Italian instruments (Hohner, Zupan, Scandalli, Paolo Soprani, Fratelli Crosio, Pigini, Victoria..). (Zupan is Slovenian, though; and Weltmeister is 'West-European now. and it seems that their quality has improved). For some brands, the year in which the accordion was made is very important: for some, old accordions are ok, but newer ones have been 'cost-optimised', resulting in a lesser quality. Then again, for others brands the quality has increased over the years.
Hohner is huge, and spans the whole price range. Its top instrument is the Hohner Gola. After that comes the Morino. At the other end of the spectrum, Hohner has imported cheap Chinese instruments, and relabeled them; they might have used a separate B-brand name for that (different from Hohner), though.
US American accordions usually are Italian accordions, either imported directly or imported in parts and assembled in the US. An example is Titano; Titano is a good brand by the way (and so is Pancordion). And Italian accordions are (were) almost without exception made in the town of Castelfidardo.
For diatonic accordions (with usually two rows of buttons both left and right), 'good brands' are Castagnari and Saltarelle.
For concertinas, Wheatstone and Lachenal are 'good' brands. Bastari/Stagi/Hohner/Gremlin/Titano etc. concertinas are factory-made Italian concertinas - closer in internal construction to accordions than real concertinas - and have little resale value compared to a vintage handmade concertina of English manufacture. Collin Dipper's instruments are quite ok again: he's got a waiting list of about two years!
As for bandoneons, I am not really familar with those; _the_ brand seems to be Alfredo Arnold, and then specifically the ones that were made around 1925. The first name is important: his sons/nephews/etc. also made bandoneons. Oh, and it should be a full size instruments, of course.
Size and possibilitiesFinally, the value depends on the size and the possibilities of the accordion. A diatonic accordion is usually worth less than a piano accordion, and small piano accordions are worth less than large piano accordions. That does not seem to be true for diatonic accordions, though: there, as long as the number of buttons and registers is the same, the smaller the box, the more expensive it is. Also, concertinas might be small, but that doesn't mean they are cheap. Don Nichols once said that his Wheatstone concertina was more expensive than his pickup truck!
For piano accordions, the thing you need to know is the number of bass buttons, and the number of registers in the treble and in the bass, and the number of voices on each side, i.e. how many reeds are maximally coupled to one button/key.
A full size accordion has 120 bass buttons, 6 rows of 20. If it has more buttons, it is probably a free bass instrument (a.k.a. Manual III, a.k.a. bariton basses), and that is more expensive. But usually owners of free bass instruments know what they have, so you won't find that one in the back of your attic; also, apart from a few early models they were invented/ developed only around 1960 (a later innovation is the converter, in which you can switch between the standard 'Stradella' basses and free basses; that saves on buttons and weight). If it has less than 32 bass buttons, it is a toy, basically; if it has got 32 or 48 bass buttons, it is probably a (cheapish) student model. 'Professional' models start at 60 bass buttons, although some professional 'high octane' players play 48 bass instruments on stage: they are easier to run around with...
Apart from the number of basses, what is the number of registers? i.e. what is the number of switches on the right hand side? Often switches are duplicated (for easier access), so look for the number of switches with different names/dot patterns. Some cheaper instruments have two voices (two reeds per key) and no registers; for (fairly modern) instruments you can easily figure out the number of voices from the register switches: they will show a number of dots, each representing voices that will be turned on for that particular switch, so the number of voices is the maximum number of dots on one switch. That switch is the master switch. Does the instruments have chin registers (buttons on the top of the keyboard) and/or thumb/wrist registers as well (behind the keyboard)? In that case, the instrument will be nearer to the top of the range
On the bass side, the number of voices is harder to guess. If the right hand side has to or three voices, the bass side will probably have four voices; if the right hand has four, the bass might have four or five.
So now some figures, please120 bass piano accordions in good condition start at about USD 300, but you might find old, 2-voice instruments for about USD 100; on the other hand, full size, 3/4, 3/5 or 4/5 reeds, 120 bass instruments of a good brand are a bit more expensive. Also, refurbished, guaranteed instruments will be more expensive than 'as is' instruments, of course.
I paid about USD 150 (after conversion) for my 32 bass Hohner Student, and USD 400 for my 80 bass Parrot. That is in the Netherlands, though; prices might differ per country.
The high end of the range is pretty high: I've seen second hand Hohner Gola 404-s advertised for around DEM 20 000 (ca. USD 10 000). And _the_ top of the line instrument is the Pigini/Yupiter Super Bayan, Friedrich Lips plays one of those. I believe that (new) that one retails for around USD 50 000! Unfortunately, these are never the ones you find in the attic :-)
To get a better idea, have a look at my list of shops, some of them sell second hand accordions, and have a second hand catalog on-line. In particular, The House of Musical Traditions, Elderly and The Button Box, and Ernest Deffner, Inc. do. All pages but the last list prices.
Of course, you could try to find a local shop; The Accordion Yellow Pages, lists addresses of (amongst others) manufacturers and retailers, and repairers.
If that fails, you could ask your question on the newsgroup rec.music.makers.squeezebox, giving as detailed information as possible. It is easier to make an estimate if one knows the number of bass buttons etc; especially if you want to know more about your obscure brand, that could help. It doesn't always, though: some brands are so obscure that noone knows them anymore; also, to estimate the value of the condition, it is vital to know its condition, and for that you would really have to see the instrument.
If you need an exact answer, some companies will do an official appraisal, based on physical inspection of the instruments; for instance Ernest Deffner, Inc. (for USD 30.- or thereabout).