Canon did enter the mirrorless market a few years ago, in the form of the EOS M, but it did everything wrong. Apparently, auto-focus was awful, so much so that I didn't even consider the camera. Peng-Toh did buy one, but he was disappointed. The one thing that Canon did right, apparently, was that the image quality was superb, but that was apparently insufficient to overcome all the other flaws.
Canon had an EOS M3 sale during the holidays (and it's still running today). At $430, it's not cheap (though in the same ballpark as say, the Sony A6000), but online reviews indicated that Canon had solved the autofocus issues with the camera. The photo community seems to think that Canon isn't serious about mirrorless, and to some extent they're right: there are only 4 dedicated EFM lenses, and the M3 doesn't sport any high end features such as in-body image-stabilization, and Canon doesn't have any full frame mirrorless cameras like Sony.
Pit against that, however, is that for any long lens work, you might as well stick the full frame EF lenses on the camera. Sure, the lens is huge compared to the camera, and you could have shaved a couple of hundred grams off the lens if you weren't carrying so much glass, but when you have a long lens that weight difference is really lost in the noise. Furthermore, those full frame mirrorless Sony cameras are very expensive, and when you come down to the same price level of the EOS M3, you get cameras like the Sony A6000. Even a cursory glance at the sample images comparing the EOS M3 to the A6000 using the kit lens easily reveals that the combination of a Canon lens and the EOS M3 utterly destroys the Sony equivalent as far as image quality. And if you're knowledgeable, you won't be shooting with the kit lens!
With that in mind, I took the plunge and got the EOS M3 for my wife on her birthday. Along with the body, I purchased the EF-M 22/f2 and the EOS M mount adapter. We also bought and returned the EFM 18-55mm zoom. The zoom was surprisingly nice, but it had a strange color cast that I didn't find appealing.
When building a new system, my philosophy is where possible build it around primes that provide roughly a doubling of focal length. So paired with the EFM-22, I got out my ancient EF 50mm/1.8. The two lenses yield a full-frame equivalent of a 35mm lens and an 80mm lens, which nicely covers the "normal" range, with the 80mm providing a great portrait lens. The 50mm together with the EF mount weigh just 80g more than the zoom, but provide a 1.8 maximum aperture which lets you isolate a subject in its surroundings. If Canon had made a wide angle prime EF-M lens, I would have bought it as well, since that's what's missing.