We had to build a chicken wire fence around our two raised beds to keep the rabbits from eating our broccoli and cauliflower. First we tried some green mesh fencing that we got at Lowe's (or Home Depot, don't recall). The rabbits chewed threw that in less than 24 hours and destroyed more broccoli and cauliflower plants. So my significant other quickly built the chicken wire fence...but since he did it quickly, he didn't build a way for me to open it, so it's now kind of hard for me to get in the garden! I'm a lot shorter than him and it's kind of comical when I want to get in there.
We've had the chicken wire fence up for several weeks now and the rabbits haven't found a way to breach it. It's not the most attractive fence, but it's in our backyard, so we don't mind.
We do chicken wire fences around beds too, and I have to lean over them to weed/harvest. With the native rabbits here, very cute little guys, we haven't had to bury the wire. We also have deer and built 8' fencing around the garden, but of course this was before rabbits became a problem and it wasn't designed to keep them out. Although I haven't seen any for a few months - either other wildlife ate them or more likely a disease went through.