Reactivity of Alkanes
Does the tetrahedral structure of the alkanes contribute to their lower reactivity? 


Hybridization is at the center of the answer. 

Due to poor P-P overlap, it only takes something on the order of 60 kcal/mol to break a pi bond and produce cis-trans isomerization about a double bond involving ${sp^2}$ hybridized carbons, whereas it takes something like 90 kcal/mol to break a carbon-carbon single bond involving ${sp^3}$ hybridized carbon atoms with highly directional orbitals that result in strong bonds. This poorer overlap with the pi bond causes ethene to be higher in energy than ethane. Alternatively one can view ethene as a two-membered ring (ref. 1), no pi bond, just 2 sigma bonds between the 2 carbons forming a two-membered ring. It is easy to imagine that such a ring system would contain a significant amount of strain (ref. 2).  Either way (and by the way these two views of ethene are equivalent and complementary) - using a poorer overlap argument or a higher strain energy argument, we see why alkenes (and even more so alkynes) would generally be more reactive than alkanes.

From this argument we would expect that if we were to somehow increase the strain in an alkane, then we should increase its reactivity. A good example of such behavior can be found in cyclopropane.  Placing 3 "tetrahedral" carbon atoms into a ring dramatically increases the strain energy in the system (it changes the carbon hybridization too, see ref. 3) and the reactivity increases dramatically.  Indeed, cyclopropane adds bromine much like an alkene (ref. 3)

Since someone above commented that ${sp^3}$ $\ce{C-H}$ bonds are "very stable and typically do not want to react". Let me just point out that $\ce{C-H}$ bond energies vary as follows

\begin{array}{|c|c|c|c|} \hline
\ce{C-H} &amp; \text{Bond Strength}  \\  \text{bond type} &amp; \text{(kcal/mol)} \\ \hline
\ce{sp^3 C-H} &amp; 101 \\ \hline
\ce{sp^2 C-H} &amp; 111 \\ \hline
\ce{sp C-H} &amp; 133 \\ \hline
\end{array}

These bond dissociation energies (ref. 4) don't fit the observed reactivity pattern.  They indicate that an ${sp^3}$ bond is actually easier to break than an ${sp^2}$ or ${sp}$ $\ce{C-H}$ bond