Mounts can change travel speed, vertical movement, combat positioning or special utility. They are most useful when chosen for a specific job rather than collected only for completion.
Travel mounts
Fast horizontal travel can make exploration, building and repeated resource routes much more efficient.
Boss mobility
Some mounts can simplify specific arenas or movement patterns. Test whether the mount improves control before replacing a familiar wing-and-boot setup.
Utility mounts
Not every mount is about speed. Some provide unusual movement or environmental utility that becomes valuable in specific tasks.
Progression timing
Compare mounts available at your current stage. A late-game mount does not solve an early-Hardmode mobility problem.
Mount versus accessory setup
A mount can sometimes free accessory pressure, but it can also make movement feel less flexible. Treat it as part of the whole mobility package rather than an automatic upgrade.
Source: Official Terraria Wiki — Mounts.