On occasion, I have encountered an unusual or antique piano. Some of these pianos can be quite interesting. Some of them can be O.K. as musical instruments. Others are better as living room ornaments.
Square pianos were once quite popular in the United States. They had a rectangular shaped case and a fan like stringing pattern. They were derived from the clavichord. The first piano that was manufactured in what is now the United States was a small square piano by a piano maker in Philadelphia around 1775. Since they had a range of 5 octaves, they could be made relatively small and they were suitable for the small homes that were fairly common during the time period. Towards the middle of the 19th century, the range of the piano expanded to 7 octaves and the square pianos became considerably larger. Square pianos had iron frames starting in the 1820s. Also they had a more powerful tone than the earlier square pianos. However, these improvements were not enough to overcome the fact that the square piano was limited as a musical instrument. The increased range of these square pianos made them much larger so they took up more space. Also these large square pianos were awkward to move. Most of the piano manufacturers in the United States ceased to build square pianos by around 1880 with a few manufacturers that continued to build square pianos as late as 1890 or so. Sometimes a square piano will be encountered by a piano technician that normally deals with modern upright and grand pianos. Due to the placement fo the tuning pins, these pianos are more difficult to tune.
It is often quite difficult to place a value on square pianos since musically, they were quite limited. Consequently the overwhelming majority of square pianos are of little value as a musical instrument. However, they often have value as antiques and in a great many cases, square pianos will be valued more for their appearance rather than their musical capabilities. If one owns a square piano, it would probably be best to use the services of a piano technician that specializes in antique pianos.
Overdamper action upright pianos were commonly manufactured in Europe until the 1880s. Unlike modern day upright pianos where the dampers are placed underneath the hammers, the dampers were placed over the hammers. In order to actuate the dampers on these actions, a long wire was connected from a part of the action above the key to a lever that lifts the damper off of the strings. Unfortunately, these wires get in the way of servicing the action and to make matters even worse, the damper action is also in the way of the strings. A special type of mute is needed and very few piano technicians will carry it since these pianos are not often encountered. These pianos often left something to be desired musically though there were some exceptions. Upright pianos with overdamper action were manufactured in England as late as 1954 and many of these pianos were not made very well. Many of them didn't even have an overstrung stringing pattern. The sound of these pianos is often atrocious. Many times, the cases were quite attractive. Thankfully for those that service pianos, very few overdamper action upright pianos were manufactured in the United States. This is thanks to Steinway & Sons who manufactured their first upright piano in 1862 with an underdamper action and an overstrung scale.  Not long afterwards, all the piano manufacturers in the United States that manufactured upright pianos adopted the underdamper action and the overstrung stringing pattern.
Kranich & Bach was once a known New York based manufacturer. The grands manufactured up until 1931 or 1932 had an action that was unique to the Kranich & Bach grands. These actions are often difficult to work on. They also had the tendency break easily. Consequently these pianos are of little value. However, there is hope for some of these pianos. Recently, a major New York based rebuilding outfit was successful in retrofitting an older Kranich & Bach grand with an action that is much easier to work with. If you happen to have one of these pianos and it is of sentimental value, you might want the consult a reputable piano rebuilder to find out if it would be worthwhile to have it retrofitted with an action that is much easier to work on and that won't start to break apart. Otherwise you might want to consider it a display piece.
The "Serenade" spinet was an unusual model manufactured by Krakauer Bros. of New York from around the mid- 1930s until sometime during the 1950s. The sides of case are curved and the back of the case has a wavy curve. The other unusual aspect of the piano is that the back of the piano is covered which is unlike most other vertical pianos including spinets. This meant that the piano could be placed in the middle of the room. Not very many of these pianos were manufactured and consequently they are rare. The value of them can be highly speculative. Recently, a near mint example of the Krakauer Bros. "Serenade" piano had an asking price of $15,000.

Starting in the mid to late 1930s up until the late 1950s, Hardman, Peck & Co. of New York offered the "Minipiano" spinet. They were very slim compared to the typical spinet piano (17" - 18" in depth vs. up to 27" in depth for most other spinet pianos). Their diminutive size made them quite attractive. Unfortunately they are extremely difficult to work on and good examples of these pianos are nearly impossible to find. They also did not make very good musical instruments. I would suggest giving them a pass. If you already own such a piano, consider it to be nothing more than a living room ornament.  

I'm not going to mention all of the unusual pianos that will be encountered on occasion since there are so many kinds of unusual pianos that will be encountered on occasion. If you think that you have an unusual piano particularly a square piano or, consult with a piano techincian that specilaizes in working on antique pianos since  they'll most likely have the knowledge how to tune and repair these old pianos.