Are metals soluble in water?

No, metals themselves are not soluble in water. When you place a piece of metallic iron, copper, or aluminum in water, it doesn't dissolve to form a solution. This is because metals exist as metallic lattices held together by metallic bonding or a sea of delocalized electrons surrounding metal cations. Water molecules cannot overcome these metallic bonds to separate individual neutral metal atoms and surround them, which would be necessary for true dissolution. Instead, many metals remain as solid pieces in water, though some undergo chemical reactions with water (like sodium reacting violently or iron slowly rusting) rather than dissolving.

$\hspace{3.em} \ce{Na}\textrm{(s)} + \ce{H2O}\textrm{(l)} \longrightarrow \ce{NaOH}\textrm{(aq)} + \frac{1}{2}\ce{H2}\textrm{(g)}$

The key distinction to understand is between metals as elements and metal ions in compounds. While a copper pipe will not dissolve in water, many salts of copper(II) ions readily dissolve. This distinction is crucial in chemistry: metals as elements don't dissolve because their metallic bonding cannot be overcome by water molecules, but many metal$-$containing ionic compounds do dissolve to produce aqueous metal ions. When we talk about metals in solution, we are really referring to metal ions, not the metallic element itself.