Many, many nucleophiles of very different-looking types add to the carbonyls of aldehydres and ketones, with and without acid catalysis. Using the mechanisms to keep track of similarities between them is virtually the only way to avoid getting lost.
Uncatalyzed Addition
The pattern in this reaction is direct attack of the nucleophile on the carbonyl carbon, with the H of the product OH group coming from the solvent (NaBH4, NaCN) or from an aqueous workup (other nucleophiles). Here is the generic mechanism:

The "filled-empty" interpretation is interaction of the filled p orbital on the nucleophile with the empty p* orbital of the carbonyl, which is why the p bond breaks.
The common types of nucleophiles and their 'delivery systems' are summarized in the following Table:

Acid-Catalyzed Additions
Acid-catalyzed nucleophilic additions follow two patterns:

and

Here the quotes around the proton indicate, of course, that it is supplied by some acid and does not occur 'naked' in the reaction mixture. Protonation enhances the polarization of the p* orbital toward carbon, thus facilitating nucleophilic attack.
The two reactions proceed by a common mechanism, branching only when the O of the alcohol nucleophile no longer has any protons to lose:

Possible G groups on nitrogen include: R, Ar, OH, NH2, NHAr, and others. Any alcohol can play the R''OH role, although reaction is most facile for primary alcohols. Both alcohol OH's also can come from within the same molecule: a vicinal diol, such as HOCH2CH2OH.