There are people out there already worrying that assigning /48s to end users in IPv6 is going to cause problems in the long term, matching the existing IPv4 problems with address shortages. I'm going to try and present a few ways to understand just why it's not going to happen that way.
Firstly, we'll need to think about the world population. Current figures show that we're at around 7 billion people. Taking the worst-case model the UN is prepared to consider, we're unlikely to reach more than 35 billion people worldwide before 2100. Against that, we have assigned a single /3 for unicast, and kept 5 /3 blocks in reserve.
A quick bit of maths shows us that we have 245 /48s to assign, before we have to use up more of the reserved address space. This is (roughly) 35,000 billion blocks to use. We have already determined that we're not going to have more than 35 billion people any time soon; so, let's assume that there are 3,500 billion people on Earth, or 500 times the current population. That's still enough /48s for each person to use an average of 10. So, one /48 at home (65,000 individual networks, of which a "typical" home might have two WiFi networks, one "server" network and a wired network). One /48 in the office (again, 65,000 individual networks in the office). Three /48s on the mobile network (one for each handset, plus one for your mobile broadband dongle). We're still only using 5 of the 10 we can allow after a 500 times population growth. Assume that ISP overheads (running routers and the like) cost a typical user another /48, and we're still within a safety margin.
Note also that we haven't yet permitted the use of the reserved /3s. If we have population growth well beyond that which we currently believe the planet can sustain, and we use more blocks that I have considered (I've assumed one connection at work, three mobile connections, one at home), we still have room to expand into. And it gets better: if the UN's worst-case projection is vaguely accurate, and we stabilise at under 70 billion people, we can each fill 50 /48s before we have to use some of the reserves.
In short, big numbers are hard. It's all too easy to see that the IPv6 address is only 96 bits longer than the IPv4 address, but hard to get a handle on just how much extra space that represents.