Can dendrite spines fire action potential toward the soma? I am confused about how the signal propagates from the dendrite spines toward the soma. I believe it is commonly taught that the signal diffuses "passively", i.e. electrostatically with no amplification during its path towards the soma.

But can an action potential be generated sometimes with opening of voltage-gated channels to help it propagate if the dendrite is very long for example?

Can we have zones along the dendrite with more or less voltage-gated channels so the signal would be a combination of both passive and active propagation?
This question shows a good amount of intuition.  It is true that the signal is generally thought to diffuse passively.  However, active propagation of dendritic signals is certainly an important property.  As opposed to the axon, where the action potential is generated by voltage-gated sodium (Na+) channels, in the dendrites, the voltage gated channels are calcium (Ca2+) channels (VGCC -- voltage gated calcium channels) or non-specific cation (Na+, K+, and Ca2+) channels such as the NMDA channel.  The voltage gated nature of these excitatory channels leads to a positive feedback effect similar to that of the action potential itself. However, the time course of these signals is much slower: on the order of 10s to 100s of milliseconds, as opposed to the 1ms time scale of the action potential.  These dendritic spikes or calcium spikes or plateau potentials can lead to firing of bursts of action potentials.  

As a side point, action potentials generated in the soma can actually be propagated backwards (backpropagating action potentials) into the dendrite using the same voltage gated channels.  http://www.ncbi.nlm.nih.gov/pubmed/8107777

References
Schiller, J. et al. (2000) NMDA spikes in basal dendrites of cortical pyramidal neurons. Nature 404, 285–9

Major, G. et al. (2008) Spatiotemporally graded NMDA spike/plateau potentials in basal dendrites of neocortical pyramidal neurons. J. Neurophysiol. 99, 2584–601

Cai, X. et al. (2004) Unique roles of SK and Kv4.2 potassium channels in dendritic integration. Neuron 44, 351–64

Wei DS, Mei YA, Bagal A, Kao JP, Thompson SM, Tang CM (2001) Compartmentalized and binary behavior of terminal dendrites in hippocampal pyramidal neurons. Science 293:2272–2275.

I actually have written a paper myself on the potential usefulness of dendritic plateau potentials in working memory:
Sanders, H. et al. (2013) NMDA and GABAB (KIR) Conductances: The “Perfect Couple” for Bistability. J. Neurosci. 33, 424–429  http://www.jneurosci.org/cgi/doi/10.1523/JNEUROSCI.1854-12.2013