A harpsichord is a wonderful instrument. They were most popular in the 17th and 18th centuries, though they existed at least a couple of centuries before then.
At first glance, a harpsichord ressembles a small piano, but as soon as you try playing it, the differences become apparent. First of all, the mechanism, which is much simpler and lighter than a pianos, serves to PLUCK the string, rather than STRIKE it. This results in a general lack of dynamics, though some harpsichords produce more than others, and all decent instruments can change timbre and volume, depending on how they are played.
Even with little to no dynamic range, a great deal of expression is possible - subtleties of phrasing and articulation are the most important of these, combines with artful arpeggiation and ornamentation. It is only in the hands of a neophyte or a pianist that a good harpsichord can truly be said to lack expression.
A very important thing that distinguishes pianos and harpsichords is that, while pianos generally are quite similar from one instrument to the next, harpsichords can be DRASTICALLY different. Many different schools of harpsichord construction existed, and continue in this century.
Most of the negative connotations of harpsichords - small tinny sounds, lack of reliability, lack of expressivity, etc - are actually not based on the historical harpsichord at all, but on 20th century "innovations" that, quite frankly, didn't work. Almost all modern harpsichord performances are on instruments built in a similar style to older instruments, which can be VERY loud, and hold their tuning much longer than most comparable instruments, though admittedly not as long as your typical piano.
It's important to note that harpsichords are not only used in baroque and renaissance music. They've been used many times in modern classical music by such emminent composers as Stravinsky. As well, there has been a smattering of popular musicians that have attempted it, most recently, and in my opinion, most convincingly, Tori Amos.
The jazz world has also seen a bit of experimentation with harpsichords as well, though most of them have been quite silly. I have yet to hear someone approach jazz harpsichord as a harpsichordist rather than a pianist trying something new. But perhaps it shall happen soon!