the hydrophobic effect
Shake a bottle of oil and water and the droplets quickly find each other and merge back into one layer. It looks as if the oil drops are attracted to each other, but the truth is sneakier: it is the water pushing them together. This water-driven clustering of oily things is the hydrophobic effect, and it is the main force that folds proteins and builds cell membranes.
Water molecules love to hydrogen-bond with each other. When an oily (nonpolar) molecule sits in water, it cannot offer any hydrogen bonds, so the surrounding water molecules have to arrange themselves into a more ordered cage around it to keep their own bonding intact. Nature dislikes this loss of freedom (it lowers entropy). So when two oily patches come together, the water cages around them merge and shrink, freeing up water molecules to roam and bond normally again. The water gains freedom, and that gain — not any direct oil-to-oil attraction — is what drives the clustering. In short, hydrophobic molecules huddle because water is happier when they do.
This effect is why a protein folds with its greasy amino acids buried in a dry core and its water-loving ones on the surface — the hydrophobic effect is the dominant driving force of protein folding. It is also why a cell membrane forms spontaneously: phospholipids line up tails-inward, hiding their oily tails from water on both sides, creating the barrier that defines every cell. Few forces in biology accomplish so much by, in effect, doing nothing but obeying water's preferences.
Drop a little olive oil into water and the scattered droplets coalesce into one blob, minimizing their contact with water — the same logic that drives the oily side chains of a protein to bury themselves in the molecule's core.
Oil clusters not from attraction, but because water prefers it.
It is misleading to picture hydrophobic molecules as 'attracting' one another — there is no special oil-to-oil force. The driving force lives in the water and its entropy, which is why the effect actually strengthens with modest heating.