How about woven leashes? I use some heavy-duty cord and do a flat weave, or a square-knot, or various other ones. You can jazz them up by painting the leash after you finish, or by incorporating larger pony beads, etc. I find that these leashes, because of the larger cord, has a high strength and doesn't break. I use something like the twine here: http://bit.ly/aV3LiC
and make simple knot weaves for a high quality leash.
What I would do:
1) Measure out your twine. I would use about double of how long you want your finished product to be, until you figure out a good rule of thumb for how much you'll actually use. I would do three to fivestrands on average, I find this makes a thin but effective leash.
2) Then fold it in the middle and start making the handle; five inches from the middle, start to braid all the strands together, either in a three-piece traditional braid or by doing an all-strand braid (will give rough tute below). Do this until you've got about ten inches of braid. Do NOT make knots at either end.
3) Now you've got between six and ten strands of string. Lay them flat on whatever surface you're working on (I usually use something I can poke a good hole through, like a spare piece of wood to nail on). Secure your handle, I nail a big nail into said piece of wood at an angle to hold the handle and to keep things together. I find this a good way to do this, especially if you're sitting--use a board long enough that you can hold it and keep THAT secure and not moving, or else you'll get a really loose product! (Which might not be a bad thing, depending on your own preferences.)
4) Start to braid all the strands together. For a flat-ish braid using all the strands, check below. You can certainly do a traditional three-piece braid like you did for the handle, or make square knots on the twine strands. Either is perfectly fine, and if you can do any other knots or braids, feel free to do it! Either way you do it, keep your twine taut and controlled, or you'll get a mess.
5) When you're down toward the end, get your heavy-gauge latch (what you'll use to secure your leash to the dog collar--available at hardware stores, online, or in your craft stores) and thread it through your twine. I find that by separating out the individual strands into two equal piles and threading the latch onto one pile, you can do some great knots to end the leash. I'd just make sure that they are tight, as flush to the latch as possible, and that you further secure your knot by adding super glue or hot glue to keep it tight. Trim any excess cord.
Voila! A leash! Like I said, you can paint your leash with pet-safe paint, like most acrylic paints. Let it dry and then you have a beautiful, home-made dog leash.
Short tute in Microsoft Paint (pic and text, sorry it's messy)
Like I said, attach the latch after you've got your braid done, knot and glue it together, and trim excess cord.