(ii) Tuning in flats: F, Bb, Eb and Ab major tunings
Depending on what type of music you play, flat keys can be quite prevalent in harp music. Some older books and tune collections (e.g. "The Small Harp" by Margaret Hewett, see Method Books) may contain quite a few tunes in flat keys. You will also run across a wider variety of keys if you choose to play Classical or Jazz, or even some Pop/Rock and New Age. For instance, I play in a trio that plays Celtic and Classical mainly, and our keys range all the way from Eb major (3 flats) to A major (3 sharps) and occasionally E major (4 sharps). For that reason, and because I also play many other styles of music, I tune my two main (nylon-strung) harps to the key of Eb, because it gives me the most flexibility. Some people will reccommend this because it offers you the maximum number of possible different keys to play in. However, some people may find they don't need an extensive range of keys, for instance if they only play Celtic, folk or early music. Some people choose to only include one or two flats - e.g., if you want to play medieval music, you will likely come across Bb fairly often, but that's about it. My wire harp is tuned to be played modally, with no sharps or flats except Bb (since I come across the Bb so often in medieval music, I've tuned my wire harp thusly: C D E F G A Bb B C). Other flat keys include Bb major (two flats, B and E) and Ab major (four flats).
Some reasons why people choose not to tune with flats are: they find that the strings don't ring quite as true with levers engaged, and/or they only play modal tunes or tunes in sharp keys, or they can't afford to have a full set of levers installed on their harp.

(iii) Tuning in sharps: G and D major
While it's not as common to tune your harp to the scale of G or D major, people who plays lots of Celtic/folk music and/or hymns will find themselves playing in these keys quite often. Frequently people who play mainly in the keys of C, G and D (and their relative minors) will tune their harp to C major, and only add levers on the F's and C's. Since levers can be expensive, this enables you to be frugal and still gives you some variety of keys to choose from. It should also enable you to play through one or two levels of beginner books with no problem (most method books and introductory books stick within these keys). The argument for this tuning is similar to the one for C major without levers (see above) - you can always re-tune your harp (and/or add levers) if you find your changing musical tastes or repertoire require it. My very first harp (a 22-string lap harp) had working levers only on C's and F's, and I played it quite happily for three years before I started to require a wider range of keys. Keep in mind that if you tune your harp to G or D (i.e. your F's and/or C's are tuned to F# and/or C#, with levers disengaged), then you will not be able to play in C major or A minor (this is why people usually tune to C and then add F and C levers to get the sharps).

(iv) Modal and Pentatonic Tuning
All of the old Greek modes can be played on a harp with no levers, tuned to the scale of C major (no flats or sharps). Modes, like any other scales, are simply a pattern of tones and semitones (e.g. if you want to play in Dorian mode, you can start on any note as long as you follow the pattern - so you can play in D Dorian, or G Dorian). For the sake of simplicity, below I've listed the main Greek modes as they would be played on a harp tuned in C:
   Ionian (same as "major"): C D E F G A B C
   Dorian: D E F G A B C D
   Phrygian: E F G A B C D E
   Lydian: F G A B C D E F
   Myxolydian: G A B C D E F G
   Aoelian (also known as "natural minor"): A B C D E F G A
   Locrian (rarely used): B C D E F G A B
The old modes listed above can be found in many types of music, from many different centuries. People wanting to play medieval music on the harp will often stick to playing in modes, however many of the modes can also be found in modern music. Dorian and Aeolian, for instance, are quite common in Celtic music (and other folk music), as is Myxolydian.
A pentatonic scale is a five-note, or "gapped" scale, e.g. C D E G A C (like a major C scale, but missing the F and B). A pentatonic tuning is probably the most restrictive in terms of limiting the different kinds of tunes you can play, but may be appropriate if you are exclusively playing one kind of music on that particular instrument. It may also be used on a very small instrument, such as a lyre or miniature harp. Pentatonic tunes are actually quite common, especially in folk and roots music.