This abstract concept is one that seems to be relatively rarely found compared to how common it is in English. Maybe it is cultural thing? Depending on the form of expression different words are found. For example, in the context of a state of mind the word intersum (to lie between) is sometimes used:
Interest scire quale senatus consultum fuerit ("It is interesting to know what kind of decree the senate made")
When we describe an object or thing as being interesting, then the adjective iucundus (as mentioned in other answers) is common. A similare adjective is gratus:
sermones inferet vel gratos vel novos ("It will introduce discussions that are interesting and novel")
Another possible adjective is curiosus. For example:
Acci positum curiose ("Accius has put in an interesting way") --Varro
Often the idea is expressed indirectly, such as by the gerundive:
Prope oblitus sum quod maxime fuit scribendum ("I almost forgot the most interesting thing of all", literally what must written) --Cicero
quidquid visendum atque memorabile ex antiquitate duraverat ("Whatever is interesting [=must be seen] and memorable which has lasted from antiquity")