Panniers are bags that hang to the sides of the rear or front wheels. Make sure they are reasonably waterproof and have side pockets for things you'll need frequently, such as maps. The only perfectly waterproof bags I know are Ortliebs, but they have no external pockets to avoid seams. I have agusport Quorums, which come with waterproof covers. My bags are fairly large but can be compressed or expanded by adjusting the straps.
Avoid zippers that are too small, or better, avoid zippers altogether. They tend to tear after a while. Also avoid straps sewn into the bag that hold it to the rack; no seam should carry any load or it will tear eventually. Bolted-on hooks work better. Make sure there is a clamp that holds the bag to the rack; a pothole might otherwise throw off the bags.
Some rear panniers are attached to each other, forming an upside-down U shape. This makes them much easier to carry over one's shoulder. My previous bags (Robens 1000 Kilometer) were of this kind, and also included a detachable backpack (a *very* good idea), but unfortunately they had lots of flimsy zippers and seams and so only lasted some 15,000 km. Choose the bags large enough so one remains at least one-quarter empty when fully packed. You'll need the space for food when riding.
I do not like front panniers because I do not like weight on my front wheel that makes steering more sluggish. I prefer packing less instead. If you ride very long distances (>2000 km) in cold or wet areas where doing laundry is impossible, you may need to pack so much that you have no other choice though.
Unless you decide to buy Ortlieb bags, pack everything into plastic bags. This makes it easier to find things, too. I usually pack all clothing into the right bag, and tools, maps, and other items into the left bag. This leaves space in the left bag for food, and it ends up smaller than the right one, allowing a better view from my bar-end mirror.
I always travel with an extra cylindrical Ortlieb bag on top of the rear rack that holds my sleeping bag and other things that absolutely must stay dry.
see also the article for "after the accident"
