If I need to carry a load on my bike, panniers are my preference. I love the feeling of having my body completely free while cycling. It makes me feel boyish, and reminds me of exploring by bike when I was young and the marvellous expansion of freedom that involved. Sometimes when cycling I'm almost amazed at the fact that I'm going so fast and so smoothly with such little effort - even though I've done it a million times before. It's like when an old couple look into each others eyes and fall in love all over again - the innocent thrill of cycling has a habit of reccuring.
Anyway, back to the topic. My second choice of bag would be a rucksack. The double straps still offer quite a lot of freedom, so you can easily forget you're carrying anything. Somehow, you don't feel heavier, despite your extra load.
Some people swear by messenger bags. I like them, but I do feel as if they're not quite as securely in place as a rucksack, since they can revolve around your body. Admittedly they probably look the coolest - if that's important to you.
Baskets are another good option. Front baskets are probably the most popular but they do suffer from the drawback that the heavier the load they carry, the more the steering is affected. Back baskets less so, but they are a little trickier to fit.
They great thing about having a basket on your bike is that you've always got some luggage capacity, so you can carry things safely (much of the time, anyway) even if you haven't prepared to do so. This is a useful insurance: because the very worst thing to do is to not bother getting a proper cycle bag or basket, and just dangle luggage - carrier bags, or any other objects - on the handlebars. This is so dangerous, and affects your control of the bike very badly. Don't even be tempted to do it.