There are plenty of camera and lens options to consider within the compact mirrorless interchangeable lens variety. Bearing in mind that all of these systems are significantly smaller and lighter than typical DSLRs, I'll leave the specific choice to your personal preference. Your options include Canon's EOS M, the Nikon 1 series, the Olympus PEN models, Fuji's X-Pro, the Panasonic LUMIX line, Sony's NEX cameras and the Pentax Q and K-01.
Perhaps the real consideration for backpacking comes from focal length options. Bear in mind that a single lens that covers a large focal range is the best way to keep your kit light, and if you can get a telephoto with an equivalent of 300mm or greater you can have success photographing some wildlife, while landscape shooters will want a lens that gets as wide as at least 35mm (in equivalent terms), though 24mm will be even more useful.
Even though ounces count, it's hard to not recommend carrying a tripod. This is especially necessary if you're interested in shooting landscapes, even more crucial if you hope to capture long exposures. The good news is the tripod can be small and compact since the cameras themselves are so small. Even more compact than a small tripod is a Gorillapod. The device can not only function as a tabletop version of a traditional tripod, but its flexible legs can be wrapped around a tree branch or other structure to provide more variation in camera angles than you could achieve with a traditional full-size tripod. And it's compact enough to fit perfectly in a backpack.
While I normally recommend a cable release for photographers who want the sharpest images they can achieve, in this case I'm going to suggest that you sacrifice the cable release and rely instead on the camera's self-timer to create hands-free exposures. It'll save some precious space in your backpack, and with a two-second self-timer you've got plenty of time to press the shutter release and get your hands off for a shake-free long exposure.
A good outdoor photographer knows that filters are crucial for landscape success. So, ensure your lenses have threads for accepting filters, then determine the filter size and head to your local camera store to stock up on a few essentials. First, the polarizer. It's a great way to get beautiful color as it eliminates reflections on leaves and other areas of the scene to allow vibrant color to shine through. It also creates deep blue skies when used correctly, and can help you create a slower shutter speed for long exposures to create storytelling motion blur. A neutral density filter, however, is the best way to do this. Let's say you want a long-exposure of a waterfall or a rushing river. With a two-stop ND filter you can cut out two full stops of light, taking an exposure of, say, 1/15th at f/32 down to a quarter of a second. A four-stop filter, as you can imagine, helps even more, or you can consider a variable ND filter to get one filter that accomplishes multiple things. The other filter you might consider is a close-up filter that stands in for a macro lens, allowing you to get super-close to flowers and insects and other small subjects that might call for a close-up. Oh, one more thing about filters: good salesmen are likely to convince you that you need a UV filter or skylight to protect your lenses. I say skip it. Save the weight and avoid this filter unless you're especially rough on your gear.
Lastly, if you're traveling for extended periods of time, or in especially harsh conditions, you'll want to address two things not only for yourself but for your equipment: warm and dry. I'll let you figure out how to keep your body warm and dry, but for electronic equipment there are a few concerns. First, the batteries. Obviously, you want to keep them dry—just as you will the camera and lenses—but you also need to keep backup batteries warm if you're traveling in winter. To do this, a good plan for your battery is to keep it in a pocket close to your body so that your body will keep it warm and functional. If you're only carrying one to save on weight, you'll have to pop it in the camera any time you're ready to shoot, but if you happen to carry a backup you'll always have a warm battery in reserve should the temperature dip so low as to render your cold battery unresponsive. Oh, and when it comes to keeping your gear dry, you can certainly invest in weatherproof packs, dry bags to insert in those packs, and silica packs to help suck any moisture out of a camera compartment. These are all great plans, in fact, if you'll be traveling for a long time or in a particularly rainy locale. But, if you just want to play it safe in case of a pop-up shower, simply tuck a few sealable sandwich bags and trash bags into your pack for use in case of emergency.