What are models for?   Most developers and users of models, in my experience, seem to assume the answer to this question is obvious and thus never raise it.   In fact, modeling has many potential purposes, and some of these conflict with one another.   Some of the criticisms made of particular models arise from mis-understandings or mis-perceptions of the purposes of those models, and the modeling activities which led to them.
Liking cladistics as I do, I thought it useful to list all the potential purposes of models and modeling.   The only discussion that considers this topic that I know is a brief discussion by game theorist Ariel Rubinstein in an appendix to a book on modeling rational behaviour (Rubinstein 1998).  Rubinstein considers several alternative purposes for economic modeling, but ignores many others.   My list is as follows (to be expanded and annotated in due course):

• 1. To better understand some real phenomena or existing system.   This is perhaps the most commonly perceived purpose of modeling, in the sciences and the social sciences.
• 2. To predict (some properties of) some real phenomena or existing system.  A model aiming to predict some domain may be successful without aiding our understanding  of the domain at all.  Isaac Newton’s model of the motion of planets, for example, was predictive but not explanatory.   I understand that physicist David Deutsch argues that predictive ability is not an end of scientific modeling but a means, since it is how we assess and compare alternative models of the same phenomena.    This is wrong on both counts:  prediction IS an end of much modeling activity (especially in business strategy and public policy domains), and it not the only means we use to assess models.  Indeed, for many modeling activities, calibration and prediction are problematic, and so predictive capability may not even be  possible as a form of model assessment.
• 3. To manage or control (some properties of) some real phenomena or existing system.
• 4. To better understand a model of some real phenomena or existing system.  Arguably, most of economic theorizing and modeling falls into this category, and Rubinstein’s preferred purpose is this type.   Macro-economic models, if they are calibrated at all, are calibrated against artificial, human-defined, variables such as employment, GDP and inflation, variables which may themselves bear a tenuous and dynamic relationship to any underlying economic reality.   Micro-economic models, if they are calibrated at all, are often calibrated with stylized facts, abstractions and simplifications of reality which economists have come to regard as representative of the domain in question.    In other words, economic models are not not usually calibrated against reality directly, but against other models of reality.  Similarly, large parts of contemporary mathematical physics (such as string theory and brane theory) have no access to any physical phenomena other than via the mathematical model itself:  our only means of apprehension of vibrating strings in inaccessible dimensions beyond the four we live in, for instance, is through the mathematics of string theory.    In this light, it seems nonsense to talk about the effectiveness, reasonable or otherwise, of mathematics in modeling reality, since how we could tell?
• 5. To predict (some properties of) a model of some real phenomena or existing system.
• 6. To better understand, predict or manage some intended (not-yet-existing) artificial system, so to guide its design and development.   Understanding a system that does  not yet exist is qualitatively different to understanding an existing domain or system, because the possibility of calibration is often absent and because the model may act to define the limits and possibilities of subsequent design actions on the artificial system.  The use of speech act theory (a model of natural human language) for the design of artificial machine-to-machine languages, or the use of economic game theory (a mathematical model of a stylized conceptual model of particular micro-economic realities) for the design of online auction sites are examples here.   The modeling activity can even be performative, helping to create the reality it may purport to describe, as in the case of the Black-Scholes model of options pricing.
• 7. To provide a locus for discussion between relevant stakeholders in some business or public policy domain.  Most large-scale business planning models have this purpose within companies, particularly when multiple partners are involved.  Likewise, models of major public policy issues, such as epidemics, have this function.  In many complex domains, such as those in public health, models provide a means to tame and domesticate the complexity of the domain.  This helps stakeholders to jointly consider concepts, data, dynamics, policy options, and assessment of potential consequences of policy options,  all of which may need to be socially constructed. 
• 8. To provide a means for identification, articulation and potentially resolution of trade-offs and their consequences in some business or public policy domain.   This is the case, for example, with models of public health risk assessment of chemicals or new products by environmental protection agencies, and models of epidemics deployed by government health authorities.
• 9. To enable rigorous and justified thinking about the assumptions and their relationships to one another in modeling some domain.   Business planning models usually serve this purpose.   They may be used to inform actions, both to eliminate or mitigate negative consequences and to enhance positive consequences, as in retroflexive decision making.
• 10. To enable a means of assessment of managerial competencies of the people undertaking the modeling activity. Investors in start-ups know that the business plans of the company founders are likely to be out of date very quickly.  The function of such business plans is not to model reality accurately, but to force rigorous thinking about the domain, and to provide a means by which potential investors can challenge the assumptions and thinking of management as way of probing the managerial competence of those managers.    Business planning can thus be seen to be a form of epideictic argument, where arguments are assessed on their form rather than their content, as I have argued here.
• 11. As a means of play, to enable the exercise of human intelligence, ingenuity and creativity, in developing and exploring the properties of models themselves.  This purpose is true of that human activity known as doing pure mathematics, and perhaps of most of that academic activity known as doing mathematical economics.   As I have argued before, mathematical economics is closer to theology than to the modeling undertaken in the natural sciences. I see nothing wrong with this being a purpose of modeling, although it would be nice if academic economists were honest enough to admit that their use of public funds was primarily in pursuit of private pleasures, and any wider social benefits from their modeling activities were incidental.
  

POSTSCRIPT (Added 2011-06-17):  I have just seen Joshua Epstein’s 2008 discussion of the purposes of modeling in science and social science.   Epstein lists 17 reasons to build explicit models (in his words, although I have added the label “0” to his first reason):

0. Prediction
1. Explain (very different from predict)
2. Guide data collection
3. Illuminate core dynamics
4. Suggest dynamical analogies
5. Discover new questions
6. Promote a scientific habit of mind
7. Bound (bracket) outcomes to plausible ranges
8. Illuminate core uncertainties
9. Offer crisis options in near-real time. [Presumably, Epstein means “crisis-response options” here.]
10. Demonstrate tradeoffe/ suggest efficiencies
11. Challenge the robustness of prevailing theory through peturbations
12. Expose prevailing wisdom as imcompatible with available data
13. Train practitioners
14. Discipline the policy dialog
15. Educate the general public
16. Reveal the apparently simple (complex) to be complex (simple).

These are at a lower level than my list, and I believe some of his items are the consequences of purposes rather than purposes themselves, at least for honest modelers (eg, #11, #12, #16).
References:
Joshua M Epstein [2008]: Why model? Keynote address to the Second World Congress on Social Simulation, George Mason University, USA.  Available here (PDF).
Robert E Marks [2007]:  Validating simulation models: a general framework and four applied examples. Computational Economics, 30 (3): 265-290.
David F Midgley, Robert E Marks and D Kunchamwar [2007]:  The building and assurance of agent-based models: an example and challenge to the field. Journal of Business Research, 60 (8): 884-893.
Robert Rosen [1985]: Anticipatory Systems. Pergamon Press.
Ariel Rubinstein [1998]: Modeling Bounded Rationality. Cambridge, MA, USA: MIT Press.  Zeuthen Lecture Book Series.
Ariel Rubinstein [2006]: Dilemmas of an economic theorist. Econometrica, 74 (4): 865-883.