In general, the rule of thumb for plants near buildings you want to keep secure is, “Don’t,” simply because plants afford people places to hide either themselves or some form of nefarious device. No, seriously, the average truly-“secure” building will almost invariably have no plant life near it aside from average grass, and in some cases those buildings have a perimeter of gravel about six feet wide leading up to their external walls.
Obviously, this does not work well with the modern American residential version of landscaping, so certain compromises have to be made.
A good middle starting point, though, is “Do not let your bushes get large enough by or under your windows to let a person hide in them easily.” Doors are typically the preferred entrance method for criminals, but windows are a very close second, and giving individuals of ill intent all the concealment and privacy they need to defeat your window locks is never a good idea. The image to the right shows an adequate example of what not to do, both with the yellow bushes at the foreground and the purplish ones in the back. Our successors at that house ended up ripping out both groups of bushes entirely.
Another good concept is this: it is entirely possible to make your against-the-house plants… inhospitable to the average person. Holly and rose bushes are natural starting points, but there are even more creative options available as well.
If you have ever visited the Pacific Northwest, you might be familiar with the adequately-named “Devil’s Club” plant, but it only grows in the rain forests out there (and, oddly, around the Great Lakes). A much more flexible, and almost equally as pokey, plant is the Pyracantha genus of evergreen shrubs – they are technically invasive here in North America, but they manage to be massively thorny while still arguably ornamental. Depending on where you live, palm trees, blackthorn, cacti, bougainvillea, yucca, barberry, locust, acacia, hawthorn, and mesquite are all options as well.
Obviously you will want to exercise appropriate caution when working with these plants, and invest in a good pair of gloves and a thick long-sleeved shirt. Likewise, you will still want to keep these bushes and trees under control, both in terms of size, but also with considerations to protecting your foundation from roots or your siding from vines.
Equally obviously, none of these will actually stop someone interested in breaking into your house or hiding against it while they do their work. However, as with all of the other security measures I have talked about here, this is making the cost/benefit analysis tilt in a way that encourages your hypothetical aggressor to find a softer target.
Or, at least, a less prickly one.