Instead of forming a neutral enol, the ketone reacts with hydroxide to become a negatively-charged enolate. The key to this reaction are the hydrogens on the alpha-carbon. Remember, that's the neighbour to the carbonyl group. These alpha-hydrogens are acidic, while the other hydrogens in carbonyls aren't acidic enough to be removed by a base. When the alpha-hydrogen is deprotonated, the anion that forms is resonance-stabilized.

Let's look at the relative acidity of alpha-hydrogens in different molecules for a moment, because this is going to introduce fun new compounds. Remember, the lower the pKa value, the more readily the substance donates a proton, and the more readily an enolate will form. 

The pKa of the alpha-hydrogens in simple, alkyl-substituted aldehydes and ketones like acetaldehyde and acetone are in the high teens, but the pKa of the alpha-hydrogens in compounds with two carbonyls are lower, so those protons are more acidic, which makes sense, with two carbonyl groups flanking them to stabilize the negative charge in the anion. 

However, the alpha-hydrogens in esters have a higher pKa than their ketone cousins. This is because there's resonance donation from the oxygen of the alkoxy group towards the carbonyl. This makes the carbonyl more electron-rich already, and it's harder to stabilize an enolate.

And it's a similar story with amides: the nitrogen donates electrons to the carbonyl  through resonance, so, again, the oxygen of the carbonyl has quite a bit of negative character. The pKa of dimethylacetamide, or DMA, is a whopping 30. We're not going to get enolates very easily from these.

So, overall, if we react a carbonyl compound with an appropriate strong base, we get resonance-stabilized anions called enolates, which are great nucleophiles - even better than enols, which are pretty good themselves.

We can see the nucleophilic power of enolates if we look at halogenation reactions. Both aldehydes and ketones will react with a diatomic halogen like bromine at the alpha position, in the presence of a base.

Like I said, this enol acts as a less aggressive nucleophile than our enolate last time. So, an electron pair attacks the bromine, and forms a resonance-stabilized cation. Finally, the carbonyl group loses its proton, and leaves us with the alpha-halogenated product we wanted - no out-of-control halogenations here. Yay!

Now, halogens are nice and all, but as you know by now, we organic chemists love to see carbon-carbon bond formation. If we introduce enolates to an alkyl halide or a tosylate, they undergo an alkylation reaction, joining the two smaller pieces into one bigger molecule.

What's happening is that the nucleophilic enolate ion is reacting with the electrophilic alkyl halide, in an S_N2 reaction, and the leaving group is displaced by a backside attack. But, because of this, we run into the usual issues that we have with SN2 reactions - namely, the alkyl group should be primary, or methyl. This reaction isn't great with secondary alkyl groups, because we start to get a  competing E2 reaction - and with tertiary, the E2 reaction is all we get.

There's one more thing we have to look out for in these alkylation reactions with enolates. Because they're resonance hybrids, they kind of have a dual identity, and two different ways of reacting.

One part of the hybrid is a vinylic alkoxide - that is, a carbon-carbon double bond with a negatively-charged oxygen attached. In this situation, enolates react at the oxygen, and we end up with an enol derivative. But, the other part of the hybrid is the alpha-keto carbanion - that is, a carbonyl group bonded to a negatively-charged carbon. In this situation, enolates react at the carbon, giving us an alpha-substituted carbonyl.

We can often favour the reaction at carbon by carefully choosing our reaction conditions. But all these complications with enolates and alkylation could lead to something that really annoys chemists: mixtures of products. If only we had a more reliable way to add some carbons to our carbonyl...

Never fear, acetoacetic ester alkylation is here!