Well, workplace environments are perhaps the most obvious example, or at least the first one I could think of, where for certain classes of user it would be very useful to be able to install packages as a non-root user. But shared hosting is another good example: my Web host will let me compile stuff, but if I wanted to install a system package in my area, it would be incredibly difficult (if not technically impossible). That this arrangement could potentially lead to me running outdated or insecure software is surely something that the hosting provider would rather avoid. Interestingly, SourceForge has started to discontinue various centrally-maintained hosted applications in favour of people installing their own versions in their own hosting areas: a concrete example of this counterintuitive trend in action.
Of course, I could choose to use a virtual private host instead, or something that provides some lighter form of virtualisation - perhaps OpenVZ or Linux-VServer - but I have to admit that I wouldn't know whether the latter solutions would necessarily give me access to package installation tools or whether I'd still need to bother the central administators.