Rationalising the order of reactivity of carbonyl compounds towards nucleophiles
Here is my "old school" explanation.  

Below is a drawing of the reaction coordinate for nucleophilic attack at a carbonyl carbon. The energy well for the starting carbonyl compound is shown on the left.  As the positively-polarized carbonyl reacts with (forms a bond with) the nucleophile we pass over a transition state and fall into a second potential well representing the tetrahedral intermediate.  $\ce{E_{act}}$ is the activation energy required to pass over the transition state.  To whatever extent a substituent might stabilize the starting carbonyl compound, the energy of the carbonyl compound will be lowered, and consequently $\ce{E_{act}}$ will increase.  The central carbon (it was the carbonyl carbon) in the tetrahedral intermediate is fully saturated (just $\ce{sp^3}$ bonds) and without charge, so the substituent X cannot interact through resonance to stabilize the tetrahedral intermediate.  In other words, while substituent X can stabilize or destabilize the starting carbonyl compound, it should have little effect on the relative energetic position of the tetrahedral intermediate.



Below are the resonance structures we can draw for our carbonyl compound.



If structure III contributes significantly to the overall description of the compound, then we would expect that carbonyl compound to be more stable, lower in energy, than a carbonyl compound where structure III contributes little.  

Let's start by comparing the ester to the amide.  In both cases structure III involves a 2p-2p pi bond, but the resultant positive charge is placed on oxygen when we start with the ester and on nitrogen when we start with the amide.  Clearly, for electronegativity reasons, the amide case is better with the positive charge on the less electronegative amide nitrogen.  Our prediction: the amide is more stabilized than the ester and therefor should be the slower reacting of the two.

$$\ce{ester &gt; amide}$$

In the case of the carboxylate anion, resonance structure III is equivalent to resonance structure I (note: there is no positive charge in structure III for the carboxylate case).  Since they are equivalent, they carry high weight stabilizing and in describing the carboxylate anion.  The carboxylate anion is so stabilized by resonance structures I and III that it is basically unreactive to nucleophiles

$$\ce{ester &gt; amide &gt;&gt; carboxylate}$$

There's really no difference between the ester and carboxylic acid in terms of resonance structure III contribution so we would expect them to have similar reactivity towards a nucleophile.

$$\ce{ester \sim acid &gt; amide &gt;&gt; carboxylate}$$

Let's compare the ester to the anhydride.  Resonance structure III is equally effective for both compounds, BUT, there are two carbonyls in the anhydride for the oxygen to interact with.  Therefor, the oxygen will only be half as effective at stabilizing any one anhydride carbonyl as it was for the ester carbonyl.

$$\ce{anhydride &gt; ester \sim acid &gt; amide &gt;&gt; carboxylate}$$

In the case of the acid chloride, resonance structure III involves a 2p-3p pi bond, not very effective overlap due to the size difference (also chlorine is electronegative so placing a positive charge on it is not desirable, but the poor pi overlap is what limits the contribution from structure III in the acid chloride case).

$$\ce{acid~ chloride &gt; anhydride &gt; ester \sim acid &gt; amide &gt;&gt; carboxylate}$$

For the ketone, our resonance structure III has a slightly different look, it involves hyperconjugation as shown in the following figure.



Since there are 3 hydrogens, there are three such hyperconjugated structures,  They are not super significant resonance structures, but there are 3 of them, they do place the positive charge on a proton, so they do count for some stabilization.  To be honest, I would have guessed that it creates more stabilization than resonance structure III in the acid chloride case, but I wouldn't have known where it fits between the acid chloride and the ester.  Wherever I put it, I'd put the aldehyde to its left.  There is no resonance structure III for the aldehyde.

I wind up with 
$$\ce{acid~ chloride &gt; anhydride &gt; ester \sim acid &gt; amide &gt;&gt; carboxylate}$$
and $\ce{aldehyde &gt; ketone}$ fitting in somewhere between the acid chloride and the ester