There are about 5,000 species of aquatic beetles, and I won't be including them all on this site. I've also only included certain aquatic beetles and terrestrial (Terrestrial: Insects which live on land and are fed on by trout only when they incidentally fall into the water are known as "terrestrials" to fly anglers, and they're very important in late summer.) families which I've found frequently on trout streams.
The common terrestrial (Terrestrial: Insects which live on land and are fed on by trout only when they incidentally fall into the water are known as "terrestrials" to fly anglers, and they're very important in late summer.) forms are especially important during the late summer when they get knocked into the stream in any number of ways. As far as I know there are no specific life cycle habits which toss these insects into the water in great numbers; they just become important because there are so many of them around incidentally.
Trout generally relish beetles and their imitations make great searching patterns (Searching pattern: Any artificial fly pattern used when trout that aren't feeding selectively on anything in particular. A searching pattern may be an attractor or an imitation of something specific that the fish might favor even though it's not currently hatching.).