The one plant that is the first to be planted in just about every butterfly garden is milkweed (Asclepias spp.). A host plant for the monarch and queen, it's also a decent nectar plant for a wide variety of butterflies. But move over, monarch caterpillar (below), there are other insects taking up residence in the milkweeds.
Aphids are a nearly constant presence on the tender ends. Normally the best control for aphids would be a spray like insecticidal soap, but in the butterfly garden I advise removing them with the garden hose. Luckily the aphids come off easily while the monarch eggs are sticky and not so easily dislodged. Unfortunately the aphids usually come back, so this can wind up being a daily process. Ladybugs will eat aphids so if you can attract them and keep them around, this can help too.
The other insects that enjoy milkweed are milkweed seed bugs. These orange and black bugs feed on the milkweed seeds. In the picture below, there is an adult in the upper right corner and lots of young nymphs on the milkweed seed pod. Usually there are only a few to be found and they can be picked off by hand. Occasionally, however, the population gets out of hand. You can try keeping the seed pods removed; otherwise spraying with insecticidal soap may be your only recourse.