Right now most of my paths are pea stone. Advantages to pea stone are

1) Cheap (if you have someone truck it in for you, you'll probably pay less than $10 per cubic yard)

2) Reasonably attractive

3) Traditional

For a few years I really liked it, but as time goes by I'm becoming a little disillusioned. The main problem is that weeds can sprout through the stones, even if you use landscape fabric underneath. I guess it's not a huge deal, and I've found that you can remove the weeds fairly easily with a hoe, so overall I still like the pea stone, but in the new section of the garden I have started using pavers. You can buy 8"x16"x1" pavers at Home Depot for less than $2 each. In the old garden (where the pea stone is), I have used these to frame the beds, by turning them on edge. In the new garden I'm trying something different - using them as path material. There will be no frames so to speak on the beds themselves - just pavers in the paths, and whatever isn't paved is a bed (if that makes sense).

So far I like it better because that means the beds are sunken slightly instead of raised. My soil is very well drained, so this is a good thing. The other thing is that with raised beds, some soil always falls out onto the paths, making a mess. If the beds are sunken slightly, it will just wash back in again.

-Diggity

I use shredded wood mulch. It is soft underfoot, requires almost no maintenance, and any weeds that do sprout are easy to pull. I put down an initial 3 inches and added a bit when it had compacted. After a year or two, it may need some more mulch added. If I decide to, I can shovel it out and into the beds when it has deteriorated enough and put fresh in the paths, but it's not really necessary to do that.

Hope this helps some.
Sandy

We cleared a lot of Viney Maple trees from our property and will be putting them thru a chipper. Whatever we collect from that will be spread between our beds. (Whatever else fits thru the chipper is being added too. We have a HUGE burn pile of other woody material that I would like to reduce before setting it afire.)

I have pea gravel as well. Not by choice though. I just happened to build my two raised beds in the kids play area which happens to be pea gravel.

I like the gravel but being in the kids area you can only imagine the number of small rocks I have to get out of the beds. Plus, believe it or not, the neighborhood cats like to do their thing in the rocks. This pisses me off as the kids play here. I may fully have to convert this area to more raised beds or do away with the rocks altogether.

Wade

I use pine needles...b/c they are free. I think my MIL used carpet strips years ago.

Lay down cardboard, then cover with wood chips or wood mulch.
You can get cardboard for free and you can get wood chips for free from tree trimming companies.
Or if you have a chipper and wood to chip you can create your own chips.
I'm always on the lookout for redwood, either logs or lumber, that people no longer want. Redwood is no good for firewood. Very good for mulch & chips. Chips up easily as it is a soft wood. Lasts a long time. Beautiful too. Then again probably not a lot of excess redwood in NY as opposed to CA. But cedar would work great too if you can find it. Even pine. I like what "gardener sandy" said in his/her post above...nailed it.
For my raised beds that are rectangular or square, I have been using old bricks around the perimeter as a kind of "catwalk". Better surface than the ground, easy to put down and looks sharp. Bricks I get free too. I am a "scrounger" of the first order.
Gravel is good for some garden uses; however I would not want to use it where it could get into my beds, but that's just me.

I have wood mulch between mine. As stated above it may have to be replaced but it goes into the compost so no waste. Easy to weed also. I also have a lot of dead fall this year that I plan to put into the chipper. Also have pea gravel in a couple of other paths and my dog kennel. It can be raked flat and looks good. Both work nice.

A thick layer of shredded tree branches.

It's coarse enough it lasts several years, thick enough to block weeds, lets rainwater through, and it's FREE from my shredder.

Cardboard and a thick layer of leaves. I'm considering growing a cover crop in it this fall to help w/ over all drainage by putting OM deep down.

rj, how would you grow a cover crop in cardboard and leaves?

I used cardboard and shredded mulch and I love it! Cheap and easy

Annual rye grass, buckwheat, field peas, cardboard, straw and grass clippings, alfalfa, clover...

To get rid of weeds in your walkways , you can:
1- pull the weeds up. But you don't want to bend too much(grin)
2- spray with ROUND Up. But you dont want to do this near your vegetable.

There is another way:
In a sunny, warm/hot day roll a clear plastic over your walkways. Secure it so that the wind will not move it and air will be trapped under it.The greenhouse effect will burn and kill most if not all of the weeds. This is my way.