No, unless otherwise specified in their description.
From the SRD:
Supernatural abilities are magical and go away in an antimagic field but are not subject to spell resistance, counterspells, or to being dispelled by dispel magic. Using a supernatural ability is a standard action unless noted otherwise. Supernatural abilities may have a use limit or be usable at will, just like spell-like abilities.
Maintaining a supernatural ability is a function of the ability itself. If the ability is lacking details, the closest spell may be used as a guideline to the DM.
Take Telepathy, for example:
A creature with this ability can communicate telepathically with any other creature within a certain range (specified in the creature’s entry, usually 100 feet) that has a language. It is possible to address multiple creatures at once telepathically, although maintaining a telepathic conversation with more than one creature at a time is just as difficult as simultaneously speaking and listening to multiple people at the same time.
As this is directly compared to "having a conversation" all the action rules for having a conversation apply to this new conversational mode. Therefore, as an alternative action cost is specified in the power, Telepathy does not require a standard action to activate.
As empathic link is also a "communicate" class, it also does not require actions to initiate. Ki Strike is another always-on ability, compared with the ability Abundant Step which functions like Dimension Door.
Another useful example is the Archmage:
Arcane Fire (Su)
The archmage gains the ability to change arcane spell energy into arcane fire, manifesting it as a bolt of raw magical energy. The bolt is a ranged touch attack with long range (400 feet + 40 feet/level of archmage) that deals 1d6 points of damage per class level of the archmage plus 1d6 points of damage per level of the spell used to create the effect. This ability costs one 9th-level spell slot.
Arcane Reach (Su)
The archmage can use spells with a range of touch on a target up to 30 feet away. The archmage must make a ranged touch attack. Arcane reach can be selected a second time as a special ability, in which case the range increases to 60 feet. This ability costs one 7th-level spell slot.
The wording of Arcane Fire means that it takes a standard action to use the power, whereas the wording of reach "can use" means that it, as always on, modulates the spells cast.
Generally, abilities that do not have a limitation are considered to be * suppressible* at will, rather than activatable at will, as there's no reason to not leave them on. As there are supernatural abilities that function "as if" they were spells, abilities that do not have limitations listed do not have those limitations.