Simple answer: if you're not a kit-lens-only shooter, five or six.
- Mid-range zoom (minimum 24-70mm equivalent, typically kit, though enthusiasts want something faster than kit lenses in this range)
- Telephoto zoom (minimum 70-200mm equivalent, typically the kit-lens partner, though enthusiasts want something faster than f/5.6 at the long end)
- Wide, fast prime (24mm equivalent or wider, f/2.8 or faster)
- Normal, fast prime (~50mm equivalent or wider, f/2 or faster)
- Moderate telephoto, fast prime (70-90mm equivalent, f/2 or faster)
- Macro lens (preferably 100mm equivalent or longer)
A kit with those lenses in it would let you make most of the general images you'd want. Wildlife, sports, and some event shooters would need more or different lenses, but you'd be surprised how much you can do with just that simple set.
So how do the mirrorless mounts fare?
- Canon EOS M: Only has a fast moderate wide prime, a wide-angle zoom, several mid-range kit lenses, and a telephoto zoom. Can use EOS lenses via adapter to provide macro and perhaps some telephoto capability.
- Fujifilm X-Pro 1, X-Pro2, XA-1, XM-1, XM-2, XE-1, XE-2, X-T1, X-T2 (X): Has seven mostly fast primes, a macro lens, plus a small handful of good zooms.
- Nikon 1 (CX): Has the three basic zooms (kit lenses), a superzoom, and a super telephoto zoom. Their first prime was not wide enough; their second prime was a normal lens that is near perfect (18.5mm f/1.8). Their third was an expensive and superb moderate telephoto (32mm f/1.8). The system is missing a macro, though you can use the 40mm or 60mm Micro-Nikkor on an FT1 to solve the problem, and solve it in spades. Still missing a fast telephoto, though it has been hinted at. Recently available is that super telephoto (70-300mm, which gets you to 810mm equivalent).
- m4/3: Has everything on the list, and many in multiple variants.
- Samsung NX: Has everything on the list, though some are in short supply and hard to find after Samsung left the camera business. Samsung lenses really don't go beyond my basic list, though.
- Sony (E-mount): By late 2012 was shipping everything on the list, though the macro lens was short in focal length (45mm equivalent). Plus only two of the lenses really start to live up to the 24mp sensor’s abilities in terms of resolution.
- Sony (FE-mount): Close to the full list now available.
As might be expected, the "oldest" of the mirrorless systems fare better than the more recent ones.
Beyond the basic lenses, things get more interesting. Technically, a well-rounded system would also have these options:
- Fisheye (180 degree diagonal capability)
- Wide-angle zoom (minimum 18-35mm equivalent)
- Full range of primes (24mm, 28mm, 35mm, 50mm, 85mm, 105mm equivalents)
- Fast mid-range and telephoto zooms (24-70mm, 70-200mm f/2.8 equivalents)
- Long telephoto zoom (300 or 400mm equivalent at long end)
And here's where we are today with that:
- Canon EOS M: the wide angle zoom was only available in some markets, for awhile, now available globally
- Fujifilm (X): wide angle zoom, fast telephoto zoom, and additional primes appeared in 2014/2015/2016
- Nikon 1 (CX): wide angle zoom came first, the long telephoto zoom appeared in mid-2014, but system appears dormant now
- m4/3: has options in all of the categories; now adding lots of overlapping and specialty options
- Samsung NX: system dormant due to withdrawal from the market
- Sony (E-mount): future roadmap unknown, but now has serious third-party lens support
- Sony (FE-mount): current lenses and roadmap have everything on the list, though could use longer telephoto now
The net takeaway, at least here in early 2017, is that m4/3 was the first to a complete set of lens options (and with many multiple choices), and was already there in 2012. Sony would arguably come close to the basic set I outline for the crop sensor models, but still has some quality issues in a few of the offerings, particularly the wide prime, and doesn’t come close for the full frame sensor cameras. Fujifilm is still a bit in catch-up mode, but they're basically there with the base set and a few extensions. Canon is a laggard, with only a few lenses available and only two known to be in development. Nikon and Samsung have stopped development.
Of course lens size and lens quality and other factors come into play when deciding between systems. But just based upon availability, m4/3 is the clear leader in terms of serving their users' basic needs, and even manages to serve extended needs well.
Note: Obviously I love choice, as do most photographers. I'm not arguing that companies should only do the lenses in the two lists, above. I'm only suggesting that those are two good starting points to evaluate whether a system offers reasonable choice. One would hope that we eventually get to the level of the DSLR systems, where 30 or more lenses are available for a mount at any given time, and the used market increases those options as lenses come and go.