For shampoo, I'd recommend going with a solid bar. They're hard to find outside of health food stores and the like, but oftentimes you can find them being sold with only a simple paper wrapping for packaging, and a $5-10 bar will easily last many times longer than bottled shampoo as long as you're keeping it somewhere where it can get a chance to dry out between showers. Conditioner is trickier; I've yet to find a solid conditioner that I like.
For detergents, we've recently switched to Dropps for both laundry and dish detergent, and I've been quite happy. It's mail order, so not zero packaging, but about as low as you can get, and they put some thought into designing a box that's easy to re-use.
For dry foods, if there's a grocery store that sells in bulk in your area, that can make a big difference. We made some cheap muslin bags that we take to the store when we're stocking up; most food co-ops and Whole Foods will let you provide a tare weight so you don't have to pay an extra $0.10 for the weight of the bag. People like to malign Whole Foods for being expensive, but their bulk section tends to be priced comparably to packaged options at traditional grocery stores.
For razors, double-edge safety razors are an option, but a bit tricky to learn to shave with. I've found I can also keep a standard Gillette Mach3 cartridge going for a good 3 months by drying it after each use (and keeping it dry - no storing in the shower), and "stropping" it on a tea towel before shaves. My hypothesis is that it's corrosion, not use, that is the main limiter of a blade's life span.