For peas I use chicken wire hooked on U-bend fence posts; sometimes I have to stack two for really tall vines. (But I'm more careful about what kind of peas I order now!
) The downside is if you do it this way you have to be able to stand on either side of the fence to pick the peas, as it is difficult to fish the pods through the chicken wire. I have also tried tying twine into nets with 4" openings like the commercially sold pea nets, but at least for the particular type of pea I grew that year that spacing seemed too large and the vines needed a lot of "help" to keep from falling over. I've thought about using chicken wire strips or chicken wire panels with holes cut out for reaching through, but I've never gotten around to trying it.
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I have not found anything a cucumber won't grow up, but they seem to particularly like chain link fencing, which is also sturdy enough to hold the melons up without sagging.
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I have tried square and round cages for my tomatoes, as well as wood and metal and plastic stakes. I haven't liked anything so far. My husband's aunt is an excellent gardener and swears by mulching with straw and letting them grow on the ground, but she has a lot more space than I do. My sister uses wire fencing with 4" openings tied in a cylinder about 2' across and 3.5' tall. She lets the vines grow as much as they want in there and cuts them if they grow out of it, and gets lots and lots of tomatoes buried inside lush little bushes, but she has a lot more sun and wind than I do - I think in my yard they would probably be prone to fungal problems and the interior leaves would waste away if I tried this method. The quest goes on...
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I tried bamboo teepees last year for my lima and pole beans and didn't have trouble with them falling over (okay, I had DH the boy scout, knot-fiend build them), but I still wasn't crazy about them. I think it was partly the varieties that I was growing, which grew very tall and required teepees with wide bases - it was just a wildly inefficient use of garden space. I also think I used bamboo poles that were a bit too stout, which caused the string beans to fall down in some places, but they grew up the thinner bamboo poles very well, so maybe I'll build some bamboo trellises this year.