A good approach is to use an everyday-looking bag with padding, or choose a camera bag designed to be low-profile.

From the suggestions given:

• A diaper bag plus a foam insert can work well. It looks ordinary, offers organization, and the insert adds protection.
• The Think Tank Retrospective series is specifically mentioned as looking non-camera-like while still fitting a lot of gear.
• Crumpler messenger/backpack options are also designed to look less like traditional camera bags and can meet your needs for padding, access, and organization.

The main tradeoff is comfort versus access: messenger-style bags are usually faster to access, while backpacks are better for carrying heavier kits over longer periods.

If your main goal is avoiding attention, the most discreet choice is often a normal-looking bag with a padded insert rather than a branded camera bag. Just keep in mind that some well-known “casual” camera bags may still be recognizable to experienced thieves.