There are lots of ways to carry your things on your bicycle. In panniers, trailers, baskets, balanced on your head, or in a back pack. There are great things about all of them (except maybe balancing things on your head) but this entry is about bags that go on your back. Although having a few drawbacks, the variety and usefulness of these bags vastly outweigh them. Carrying your load on your back lets you control the center of gravity of your bike in a leaned turn. With a load on my bike rack, I feel like my response time is sluggish and laggy. Another plus is when you get off your bicycle, your things are already with you, no carrying panniers around.
A traditional backpack has a compartment with two straps that go over each shoulder evenly. This is probably one of the most common bags for carrying a moderate amount of things. The great thing about a backpack is the stability and even load bearing over both shoulders. Especially with a waist strap these bags can be cinched down tight to keep things from shifting. There is a wide variety of size, quality, and price. There are bike-specific backpacks but any functional backpack will work. I prefer these bags over satchels for carrying especially heavy loads. Be careful loading large backpacks for a bike ride. Do not pack as if you are going hiking, placing your heavy things on top to give you better balance. On a bike, you want a low center of gravity, so put the heaviest things at the bottom. Whatever your load, make sure it is a comfortably snug fit. Your load shifting around while riding can be dangerous if it throws you off balance.
Satchels. OK, OK, Messenger Bags.
I have loved this style of bag since I got one in 6th grade. The best part about a satchel is that you can swing it around and access your load while underway. Never fear though, they have secondary straps to keep them securely on your back the rest of the time. Although they can carry quite a lot, very heavy loads might be more difficult to distribute evenly, unlike backpacks. It takes a bit of practice but just make sure you pack so you have a flat side against your back. They do come in a wide variety of sizes and setups.
Things to Look for in a Bag.
Get a bag to fit your needs. One bag will not fit all situations. I suggest getting a daily commuter bag, either a backpack or a messenger bag, depending on your preference. Make sure it is large enough to carry your daily needs but not over-large, because that can become awkward. For backpacks, one nice feature is some system to let air circulate between your back and the bag. This avoids sweaty-back syndrome. For a messenger bag, find one that fits you and feels comfortable snugged down on your back. Make sure it has closing straps to keep the top closed. Lots have Velcro but I find straps more useful and secure. Some folks prefer a release on the front strap. My first one did not have one, but my current one does, and I do really like it. Be careful with overly-clunky snaps, such as those made of seat-belt buckles, as they tend to smash onto whatever you set it down on. For all bags, look for comfy should snaps and the ability to snug them down. You don't want your load shifting. Another thing to think about is waterproofing. Though not necessary, it is a big peace of mind for me to know my things will stay dry. You can get a waterproof bag by design, or by buying a few small "dry-bags" and putting them inside your non-waterproof bag. Make sure you get a chance to try on some bags before you buy. It has to be comfortable. If you want to buy online, go around and try the bags at a local store before shopping online.
Ok, backpacks and messenger bags aren't perfect. There are a few things of which you should be aware. A backpack will raise your center of gravity, possibly making you more unstable, depending on how strong of a rider you are. I find that with my load on my back, rather than my bike rack, I have more control over the weight in a leaned turn, etc. If you take a spill, the things in your bag might get banged up, but this is true for most carrying solutions on a bicycle. Another problem is the hot back. Having a big heavy load against your back can lead to a sweaty backpack footprint left behind. Some people prefer carrying their load on a rack for that reason.
Things to Avoid in a Bag.
Don't go cheap. A good bag will last you a long time. It is better to get a good bag you are happy with, than a cheap one that will fall apart at the worst possible time. Be careful of bags with the waterproof fabric on the outside. Some people like it because it sheds water more quickly but on the other hand, it does make your back wet more quickly than a fabric-covered bag.
Don't like the price?
Make your own! I made my own commuter bag. It turned out quite well, as you can see from the photo. I based on on the large-sized Chrome bag (Kremlin, I think). It is waterproof with an internal liner. It is HUGE and I have had little I can't carry. The duck fabric on the outside keeps me a bit cooler than if it was the PVC fabric as it wicks. I love telling the folks with the $200+ Chrome bags that mine cost about $25. Be creative and have a sewing machine with a strong needle.
Some Bag Reviews:
Lots of Bags - good side-by-side comparison
Some Popular Messenger Bags (these sites also have backpacks; definitely shop around):
Timbuk2 - ballistic nylon covering, waterproof liner, padded strap, $85-135+
Manhattan Portage - ballistic nylon, straps, ergonomic, some waterproof, $50-100
Chrome - tough, waterproof, expensive but lifetime guarantee, $120-180