There certainly are ways to train without the use of treats, but I find that most dogs who are trained without aren't as happy to work for you as dogs who are trained with treats are. I train my dogs using different motivators -- they tend to get bored with the same reward over and over. So sometimes I use lots of praise, sometimes I use treats, and often I use a favourite toy. While teaching something new to any of them, I reward everytime they do the behaviour I want from them. Once they start realizing what I want, and are performing the behaviour reliably, I slowly phase the reward out, much like flatcoat described. Once they've perfected the behaviour, after a period of time, they're rarely rewarded heavily. They certainly are happy when they do get a treat, but if I tell them to sit, for example, they'll do it regardless of whether a reward is coming or not.

And as far as classes go, I completely agree with everyone who said they're a good choice. Never again will I have a dog and not go to classes, I don't think! My dogs who have been to classes are much more well rounded than the two that didn't go. I'm perfectly capable of teaching the basics at home, but I'd rather have the help of a class. Not only does the dog get to work in a highly distracting environment, but if you do need help, the trainer is always there. I've just started a formal obedience class with Dance, and even after taking quite a few different classes over the years, I still learned a few new things!