I always call that yucca.

This plant started growing by itself in my Southern Californian front yard and has been growing robustly in the full sun. Any idea what it is? Image link:

That's absolutely it! I googled that plant name and found this: http://images.google.com/imgres?imgurl=http://www.succulent-plant.com/asclepiads/asclepias/asclepias8.jpg&imgrefurl=http://www.succulent-plant.com/asclepiads/asclepias.html&h=458&w=600&sz=49&hl=en&start=15&um=1&tbnid=Hhpum2ZXnnmLrM:&tbnh=103&tbnw=135&prev=/images%3Fq%3DAsclepias%26svnum%3D10%26um%3D1%26hl%3Den%26safe%3Doff%26sa%3DG which looks exactly like my plant. Thanks for the advice. We ditched the cleome (one of my favorite flowers) and broccoli and so the orange and black bugs seem to be gone with them. I'll hunt for a eco-friendly aphid treatment. :)

I don't know what species this is. I feel confident that it's not a wasp or bee. The body shape is too different, I don't see wings (which almost certainly means the striping along the back of the animal is occurring on "elytra", the modified forewings nearly all beetles have, and which protect the hindwings actually used for flying), and the feet look very much like beetle feet. I can't see the antennae well enough to be absolutely certain, but I strongly suspect this is a longhorned beetle of some sort. There are many such beetles, some of which hang out in flowers as adults (without harming them). Very often the larvae of these beetles eat trees & shrubs, usually when those plants are already in a state of decline, or have already died. I think it's striped in a pattern that mimics bees & wasps. Many longhorned beetle species have such striping (although many more do not). I also suspect your flowers are being damaged by thrips, especially if this damage occurs most often on your pale colored roses.