So here's another blow to your perceived home security: six foot fences don't keep anybody out. Unless you have barbed wire topping it (unlikely in the suburbs), you can climb chain link like a ladder. Wooden privacy fencing isn't much better. I barely top 5 foot tall and I've jumped a few myself. So, as an added layer of security I've planted things with thorns around the fence.
My roses here look nice, and since they've grown some more since this picture was taken they're tall enough to arch over the gate. This is important because gates are easy to get past, even if you've locked them. The corners of the fence and anywhere the ugly (not smooth) side faces out are the same. If you can't plant things on the outside of the fence, plant them just inside. Roses, blackberry bushes and cactus are good choices for where I am, and I've made full use of them.
Speaking of cactus, this is a prickly pear. (Photo isn't mine) They're easy to grow- I asked a neighbor for a few pads and stuck them halfway in the ground alongside my house to make the "blind spots" bad places to hang out. Some folks also plant them under the windows as a burglar deterrant, which isn't a bad idea but bars are better.
Besides being a great living fence, prickly pear is also a food source. You heard me right. The pads (nopales) are eaten as a vegetable, and the fruits (tuna) are sweet and tasty. Use BBQ tongs to pick them and wear heavy gloves when handling them. During times of drought I've seen ranchers use a propane torch to burn the spines off so the livestock can eat them for emergency fodder.
I heard they're an invasive species in Australia, but frankly they're kind of invasive in Texas, too- and they're a native plant to us.