It really depends on the ability being used
The game has many abilities that allow opposed checks, some will say that the opponent can make a check to resist, allowing us to understand that they may refuse and automatically fail should they desire to, while other abilities will say that they must make a check to resist the effect, so they don't have an option and are required to make a check.
For instance, the Sleight of Hand skill has two uses that both are automatically resisted and may be resisted. A character trying to Hide an Object or Take Something Unnoticed is automatically opposed by whoever is observing them in action. While when trying to Palm a Weapon the observers can make an opposed check to notice what you are doing normally, but if they are actively observing your character (carefully observing), they will gain a +4 on that check.
The Perception, on the other hand, is mostly reactive, unless the character is actively looking for something, like a rogue searching for traps and/or secret doors. So when a character is attempting to sneak past another using the Stealth skill, that check is automatically opposed by the Perception skill of the guard. But if this guard is searching behind the bushes for someone quietly hidden (who succeeded on the previous check), he must spend a move action to make his Perception to notice that someone is hiding there.
For Sense Motive it depends on what kind of action is being used against the character, some will require some action, which normally takes a minute of interaction, while others will happen automatically in response to another action, such as being lied to. This was somewhat confusing in the Core Rulebook, but was later clarified on Ultimate Intrigue (pg 188):
Active and Automatic Sense Motive: Most uses of Sense Motive are active and require a character to spend a minute or more interacting with someone with the intent of using Sense Motive for a particular purpose. The only time that Sense Motive happens automatically is when it opposes Bluff, as it says in the Core Rulebook that a character attempts a Sense Motive check for every Bluff check attempted against him. See the Bluff section on page 182 for guidance on how often to call for Bluff checks.