Nucleophilic Addition of Hydrohalic Acids
As you noted, hydrogen cyanide will react with carbonyl compounds to form cyanohydrin and alcohols to form ketals/acetals. The list can be expanded to include aminals after attack of a nitrogen nucleophile, or thioacetals after sulphur attacks.

So why does it not happen with hydrogen halides? Well, in the case of the above mentioned, the reverse reaction is usually not favoured. In fact, ketals are used as protective groups for ketones (usually the reaction with ethan-1,2-diol or propan-1,3-diol); and propan-1,3-dithiol is similarly used for umpolung reactions. Likewise, the cyanohydrin has a new carbon-carbon bond formed, and these are relatively stable. To remove the ketal protective group, a rather strong Brønsted acid is often required along with an excess of water.

But in the case of a halide, that can just easily diffuse away again as a happy little halide; carbonyl double bond will be reformed. In fact, this reaction can be (and is!) used in exactly the opposite direction: liberate a hydroxide on the same carbon as a halide, and the halide will be eliminated to create the double bond.