Everyone is different. Two my be enough if you are a recreational road rider and want for nothing more... one for training and inclement weather and one for nice days and group rides when you really want to give 'er. But it all depends on your lifestyle...
Personally, I require about 7, but have 11.
The early part of this year largely consisted of winter road miles (in the fall I'll do some cyclo-cross racing) (cross bike, 1) and mountian biking (MTB, 2). I ride daily on my fixed gear with fenders to work, the store etc (fixed conversion, 3). I also play bike polo about once a week for fun and socializing (polo bike 4). As they weather becomes nicer I pull out the road bike and do some triathlons (road race bike, 5). Yesterday, I was organizing my work bench and decided I needed a hardware (nuts, bolts, and washers) organizer so I quickly jumped on my converted MTB basket porteur bike (basket bike, 6) and went to the hardware store... later that day my girlfriend and I went out for dinner and then a party and we picked up a 12 back of phillips beer and of course having the wald delivery basket was key. A couple weeks ago we went camping for 3 nights on Galiano island and need to bring all our food and supplies in with us... we like to live it up when we bike camp... so of course I needed my touring/trekking bike (tourer, 7).
My girlfriend has a polo bike, a city bike and a touring commuting bike... she has a single speed which is not necessary.
I also have 2 vintage roadies, one vintage track bike and one sport touring/rando style bike which I could live without.
Between the two of us. 10 is enough, but I am happy with 15 (11 me, 4 her)
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1 Super Record bike, 1 Nuovo Record bike, 1 Pista, 1 Road, 1 Cyclocross/Allrounder, 1 MTB, 1 Touring, 1 Fixed gear