For solids you are looking for the linear thermal expansion coefficient $α_L$:
$$α_L = \frac{\mathrm{d}L}{L\cdot \mathrm{d}T}$$
where $L$ is length and can be uniform for isotropic materials (amorphous compounds, some polymers) and varied for anisotropic materials (crystals).
For crystalline materials $L$ is often given for each axis $a, b, c$ of a crystal's unit cell resulting in direction-dependent thermal expansion.
Obviously, the higher the $α_L$, the higher the value of expansion $(\mathrm{d}L/L)$ per temperature change $\mathrm{d}T$, so the expansion of the solid is directly proportional to $α_L$.
The Engineering ToolBox provides a decent list of thermal expansion coefficients for common solids at NTP.
Looking for the materials with high thermal expansion coefficients, you probably have to look at polymers such as ethylene ethyl acrylate $(α_L = \pu{205e-6 K-1})$, ethylene vinyl acetate $(α_L = \pu{180e-6 K-1})$ or polyethylene $(α_L = \pu{108e-6 K-1}~\text{to}~\pu{200e-6 K-1})$.
Paraffin wax also has high $α_L = \pu{106e-6 K-1}~\text{to}~\pu{480e-6 K-1}$ (depends on exact composition) and expands drastically when reaches its melting point.
Among crystalline matter, the current record is held by silver(I) hexacyanocobaltate(III), $\ce{Ag3[Co(CN)6]}$ [1].
Due to mobile layer of silver atoms in between $\ce{Co(CN)6}$ sheets the crystal lattice can fold in one direction and stretch in another.
Such high anisotropy results in $α_a = \pu{130e-6 K-1}~\text{to}~\pu{150e-6 K-1}$ and $α_c = \pu{-130e-6 K-1}~\text{to}~\pu{-120e-6 K-1}$.
This is the record values for both negative and positive thermal expansion in crystals.
References
- Goodwin, A. L.; Calleja, M.; Conterio, M. J.; Dove, M. T.; Evans, J. S. O.; Keen, D. A.; Peters, L.; Tucker, M. G. Colossal Positive and Negative Thermal Expansion in the Framework Material $\ce{Ag3[Co(CN)6]}$. Science 2008, 319 (5864), 794–797. https://doi.org/10.1126/science.1151442.