What does the LHC do afterwards? Astronomical telescopes are now mega projects and cost $1Bn and although they are pitched to solve the current interest of the day they are general purpose machines and with upgrades and new instruments have a life of perhaps 50years.
It seems that large accelerator projects are built to answer one question, to find one particle. But since the design must be based around the particle having a particular energy and the cost and timescale being so large - you have to be pretty damn sure that you expect the particle to exist and at the predicted energy.  It almost seems that if you had a good enough estimate to build the accelerator then you don't really need to!
Is something like the LHC a one trick pony? You turn it on and confirm the Higgs or if not - build a bigger one?    
Is the LHC really a more general purpose experiment but the Higgs gets the press attention or is it just that the nature of discover in HEP is different and you need to build a single one shot experiment?
 A: The LHC has four main detectors and several fixed target 'sheds', the search for the Higgs is obviously the headline search but there are lots of bits of particle physics that will be refined and expanded upon by the knowledge learnt by work at the LHC.
This CERN page goes into more detail:  http://public.web.cern.ch/public/en/LHC/LHCExperiments-en.html .
Once (if!) the Higgs is found, there will be much more work to properly characterise the situation, this isn't just a case of 'bird-spotting' where we are only tryin to tick off another particle!
And as an aside some new astronomical telescopes are short term projects.  Herschel will likely have a productive lifespan of around 3 years only...
A: The LHC was envisioned as a "discovery" machine, a multipurpose one. The Higgs gets the press but the expectations is that new physics will become accessible with the higher energy available for center of mass collisions.
The Z was discovered in the SPS the proton antiproton previous generation collider. 
The previous machine in the same tunnel as the LHC,  LEP, an electron positron collider was needed to  establish with great accuracy the parameters of Z itself and  the standard model. 
In general leptonic collisions probe elementary interactions with many less assumptions than proton proton or proton antiproton machines. This is because one is throwing balls of three quarks with their gluons at each other and measures the debris, in order to study the interactions. New physics, because of the high energy, will appear, but will be  in a complexity unprecedented up to now. Hopefully the next generation will be a lepton machine that will allow to establish the appropriate models unequivocally.
Now on the question of one off detectors: CERN is practically using all the accelerators built up to now as increasing energy stages to feed the end machine, the LHC. Nothing is wasted. In addition a lot of experiments are approved and running in beam lines that are not in the mainstream but may prove valuable or have unexpected theoretical repercussions.
Thus one expects that the LHC will open the window to the new physics that is tantalizing us,strings and unification of all forces at the moment, and the next generation machines will be leptonic ones to allow accurate measurements of parameters and decide between models.
