$\ce{F}$ has more unshared electron pairs and is very electronegative, so $\ce{H}$ of another $\ce{HF}$ molecule can $\ce{H}$-bond with it.
$\ce{HF}$ has normal boiling point of $\pu{19.5^oC}$ while $\ce{H2O}$, as you know, has normal boiling of $\pu{100^oC}$.
I think there are a variety of qualitative ways of looking at this:
Experimental results are the gold standard, of course, as opposed to qualitative reasoning, and qualitative reasoning here can also lead us in the opposite direction; one might argue that by having three lone pairs, F has a lot on its plate, so to speak; it might be able to stabilize one lone pair of electrons very well but three lone pairs is a bigger ordeal, and perhaps big enough that the hydrogen bonds among $\ce{HF}$ molecules are stronger than those among water molecules. Again, this is all qualitative, but this is the sort of reasoning introductory chemistry teachers desire.
If we limit our thinking to just electrostatics then we might surmise that $\ce{HF}$ should have the stronger hydrogen bonds because F is more electron withdrawing and therefore hydrogen should be more positively polarized in $\ce{HF}$ as opposed to hydrogen in water. However, hydrogen bonding is more than just electrostatics. Hydrogen bonding actually has a covalent component; this, however is usually ignored by introductory treatments of chemistry. The bond angle of elements involved in a hydrogen bond is critical. The closer the elements involved in a hydrogen bond are to 180 degrees, the stronger the bond (this specific angle is the case with hydrogen bonding in water; not necessarily other molecules). If hydrogen bonding were purely electrostatic then this would not be the case; angles would not matter - only distance would.
Other issues must be explored as well, such as the number of viable hydrogen bonds and the electron-donating/releasing tendencies of the involved elements.
After scouring the web some common "explanations" that would not explain why water has a higher boiling point than $\ce{HF}$ would be:
water can form 4 per molecule while HF can only form 2.
Incorrect because if we only look at hydrogen bonding as involving the polarity of atoms, then how can water form four hydrogen bonds per molecule? It has two positively charged hydrogens, and a negatively charged oxygen. Seems like it should only form three hydrogen bonds. One must understand that lone pairs can each be hydrogen bond donors.
The answer lies in hydrogen bonding.
Hydrogen bond energy depends on the electronegativity of a highly electronegative atom which is bonded to hydrogen. Electronegativity of hydrogen is $2.2$, for oxygen it's $3.44$ and it's $4$ for fluorine.
Difference in electronegativity between $\ce{F}$ and $\ce{H}$ is $1.8$ and between $\ce{O}$ and $\ce{H}$ is $1.24$. Hydrogen bond energy of $\ce{H-F}$ is $\pu{41.83 kJ/mole}$ and that of $\ce{O-H}$ is $\pu{23 kJ/mole}$.
$\ce{H-F}$ bond is stronger in comparison to $\ce{O-H}$ bond. In the case of $\ce{H-F}$, there exists hydrogen bonding even in vapour state, 4 to 7 $\ce{HF}$ molecules together form one unit in vapour state. However, in the case of water, there is no hydrogen bonding in vapour state; each water molecule exists independently.
So, to boil liquid water, all hydrogen bonds have to be broken and it requires a large amount of energy. This isn't the case in $\ce{HF}$; all hydrogen bonds need not to be broken, and therefore a lesser amount of energy is required. So $\ce{HF}$ boils at a much lower temperature as compared to water.
Both fluoride and oxygen are very electronegative. When they bond with hydrogen the hydrogen becomes slightly positive and the electronegative atom slightly negative. Because of this, attraction occurs between the negative atoms and hydrogen in different molecules, called hydrogen bonding.
In water there are two hydrogen making more charge dipoles for stronger and more numerous hydrogen bonds.
Another factor is water disassociates (i.e. liquid water is partially made up of $\ce{H3O+}$ (three hydrogen and an oxygen, which is positively charged) and some $\ce{OH-}$ (one hydrogen and one oxygen, negatively charged). This increases inter-molecule interaction, making the boiling point higher.
I think we may have been focusing too much on $\ce{HF}$ and $\ce{H2O}$. If we look at the bigger picture of the boiling points of the hydrides of the elements of their respective groups, we can see that group 17 hydrides really have lower boiling points than that of group 16 hydrides. I still don't know why is the trend this way within each period, but the figure definitely tells us that:
So I think now the main question is: why do hydrogen chalcogenides have higher BPs than hydrogen halides (and is actually the group of halides that have the highest BPs in each period)?
(figure is from http://www.vias.org/genchem/kinetic_12450_08.html)
Intermolecular forces (IMFs) are the key here. IMFs are directly related to boiling point.
Both $\ce{HF}$ and $\ce{H2O}$ have hydrogen bonds ($\ce{H}$ attached to $\ce{N}$, $\ce{O}$ or $\ce{F}$). But $\ce{H2O}$ has two hydrogen bonds whereas $\ce{HF}$ only has one. Thus, $\ce{H2O}$ should have a much higher boiling point.
