Chemistry - Which chemical reactions don't involve bond breaking?

Solution 1:

The reaction of a Lewis acid with a Lewis base results only in bond formation. Your question gets at the essence of chemistry, though. A chemical reaction is the rearrangement of electrons between atoms. So generally, most reactions will involve breaking bonds. Even for monomers (e.g. alkenes) to polymerize, $\pi$-bonds within the monomers have to be broken to form $\sigma$-bonds in the polymer. You seldom have one without the other.

Solution 2:

Precipitation reactions? If you will grant me that an aqueous ion is free. (But maybe you don't and consider the solvated ion bonded to nearby water.)