We present scaling relations for the total cross sections and collision strengths of bound-state excitation in positive ions. The colliding particle can be positively or negatively charged and can be a fully ionized atom, an electron, or a positron. We consider collisions in which the kinetic energy of relative motion is large and consequently the adiabaticity parameter \ensuremath{\xi}\ensuremath{\ll}1. We illustrate our general method by calculating collision strengths for proton-impact excitation of fine-structure transitions in hydrogenlike ions. The limiting case of infinite nuclear charge is also included in our calculations. Using a unitarized Coulomb-Born approximation, we show that, for dipole transitions, colliding particles with large orbital angular momenta (l\ensuremath{\gtrsim}2000) make an important contribution (\ensuremath{\sim}70%) to the collision strength of proton-impact excitation. For a nonrelativistic projectile energy ${\mathit{E}}_{\mathit{i}}$\ensuremath{\rightarrow}\ensuremath{\infty}, we use the Born approximation to obtain the scaled collision strengths. These limiting values, dependent only on the particular transition, confirm the correct high-energy behavior of our data. We also use the interactive graphics computer program omeups [Burgess and Tully, Astron. Astrophys. 254, 436 (1992)] to extrapolate our data to higher energies.