My turtles love corn. They don't get it very often, because it's pretty high in sugar, but they probably get it about once a month through the summer.
Snap peas, I'm not sure. I know regular peas are on the "not too often" list, but snap peas are a bit different. I've tried snap peas with Ralph (raw), but with not too much success.
EDIT: I see snap peas have a Ca:P ratio of about 1:1.5 (cooked), so I would imagine they are also on the "not too often" list.
I'm not sure about asparagus, but the calcium:phosphorous ratio is about 1:2 (recommended is 2:1). It also has a high purine level (Thanks wikipedia!) which can cause gout.
I wouldn't recommend asparagus, but then, I don't like it myself
