The weak, electromagnetic, and strong fundamental forces can all be quite important, depending on the energy and distance scales of the phenomenon in question. How about gravitation? It is negligible, at least for what concerns the energies we can reach in particle accelerators (in fact, gravity is not even included in the the Standard Model). Gravity manifests its power only at the macroscopic scale or at the unreachable Planck scale.
This "puzzle" of "weak gravity" is an unsolved problem in theoretical physics, known as the Hierarchy Problem.
You can easily see that gravity is really "weak" at the fundamental level: in the static limit, the electric and gravitational force laws are both inverse square laws, so if one computes the ratio of the forces between two bodies, the distances cancel.
Take two point particles with masses $m_1$, $m_2$ and charges $q_1$, $q_2$. You have the gravitational force and the electric Coulomb force (CGS units are used)
$$
F_G = G \frac{m_1 m_2}{d^2}
\qquad \quad
F_C = \frac{q_1 q_2}{d^2}
$$
Clearly (depending on the actual values of $m_1$, $m_2$, $q_1$ ,$q_2$) you may have that $F_G > F_C$, or the other way round.
However, for (charged) elementary particles, you always have that $F_G \ll F_C$. In particular, if you use two electrons ($m_1=m_2=m_e$,
$q_1=q_2=q_e$), then you have
$$
F_G / F_C = \frac{G m_e m_e}{q_e q_e} = G \left(\frac{m_e}{q_e} \right)^2 \sim 10^{-42}
$$
where the quantity in the parentheses is the mass to charge ratio first measured by Thompson. As you see $F_G \sim 10^{-42}F_C$, independently on the distance $d$: the gravity attraction is really extremely weak.
In an Hydrogen atom you should compare the attraction between the electron and the proton (i.e. the Hydrogen nucleus). The proton is $\sim 2000$ times more massive than the electron so $F_G$ is $2000$ times bigger than the electron-electron gravitational attraction considered before. In this case you should find $F_G/F_C \sim 10^{-39}$. Still a super small number, telling us that there is no need to include gravity when studying the atomic structure.
Clearly if you don't use fundamental particles but, say, planets (that are almost neutral but have a huge mass), then $F_G$ wins. However, using planets and stars is, clearly, not in the spirit of the Hierarchy problem.
