Most of the streams you'll fish won't require wading, and, I dare say, require that you not wade or you'll spook every trout in the river. You generally don't have to ford many streams, and when you do, they are typically narrow and shallow. This being said, I still usually bring some kind of wading shoes because some of the streams are awfully cold and the better trout lie is always on the other side of the stream.
Some anglers use lightweight, stocking-foot nylon waders. These roll up and don't take much space. A disadvantage is that they aren't very durable, and could tear easily, since you'll likely be walking through brush and crawling on your knees to approach spooky trout. The lightweight neoprene waders don't roll up quite as tightly, but they are more durable and comfortable against the cold. If you like the convenience of these waders, it's a good idea to pack a repair kit (duct tape works to fix waders in a pinch).
If waders aren't your style, or you want to keep your pack weight down, try old tennis shoes to splash in the crystal-clear streams. Many anglers glue felt to the soles. Tennis shoes can be strapped onto the outside of the backpack. Disadvantages are that they get heavy when wet and do not provide any ankle support.
Another alternative is the felt-soled sandal offered in most mail-order sporting goods catalogs. These are cheap, light, and don't hold water. But they do leave toes and ankles open to sharp rocks, and they provide no ankle support whatsoever. To keep the tootsies warm, buy neoprene socks to wear under the sandals. If you keep your toes warm, you'll hardly notice the numbing cold on your calves and knees. These socks also come in handy if you choose to ford a stream in your hiking boots.
Whatever wading shoes or boots you wear in the backcountry, I highly suggest felt soles if you plan on wading rocky streams. Felt-soled bottoms won't last long if you wear them on the trail, but replacement felt is inexpensive and easy to glue on (even for a ten-thumbs like me).
Details mentioned in this article were accurate at the time of publication