I'm wondering what the value is in taking a continuous predictor variable and breaking it up (e.g., into quintiles), before using it in a model. 

It seems to me that by binning the variable we lose information.


Is this just so we can model non-linear effects? 
If we kept the variable continuous and it wasn't really a straight linear relationship would we need to come up with some kind of curve to best fit the data?


You're right on both counts. See Frank Harrell's page here for a long list of problems with binning continuous variables. If you use a few bins you throw away a lot of information in the predictors; if you use many you tend to fit wiggles in what should be a smooth, if not linear, relationship, & use up a lot of degrees of freedom. Generally better to use polynomials ($x + x^2 + \ldots$) or splines (piecewise polynomials that join smoothly) for the predictors. Binning's really only a good idea when you'd expect a discontinuity in the response at the cut-points—say the temperature something boils at, or the legal age for driving–, & when the response is flat between them..
The value?—well, it's a quick & easy way to take curvature into account without having to think about it, & the model may well be good enough for what you're using it for. It tends to work all right when you've lots of data compared to the number of predictors, each predictor is split into plenty of categories; in this case within each predictor band the range of response is small & the average response is precisely determined.
[Edit in response to comments:
Sometimes there are standard cut-offs used within a field for a continuous variable: e.g. in medicine blood pressure measurements may be categorized as low, medium or high. There may be many good reasons for using such cut-offs when you present or apply a model. In particular, decision rules are often based on less information than goes into a model, & may need to be simple to apply. But it doesn't follow that these cut-offs are appropriate for binning the predictors when you fit the model.
Suppose some response varies continuously with blood pressure. If you define a high blood pressure group as a predictor in your study, the effect you're estimating is the average response over the particular blood-pressures of the individuals in that group. It's not an estimate of the average response of people with high blood pressure in the general population, or of people in the high blood pressure group in another study, unless you take specific measures to make it so. If the distribution of blood pressure in the general population is known, as I imagine it is, you'll do better to calculate the average response of people with high blood pressure in the general population based on predictions from the model with blood pressure as a continuous variable. Crude binning makes your model only approximately generalizable.
In general, if you have questions about the behaviour of the response between cut-offs, fit the best model you can first, & then use it to answer them.]
[With regard to presentation; I think this is a red herring:
(1) Ease of presentation doesn't justify bad modelling decisions. (And in the cases where binning is a good modelling decision, it doesn't need additional justification.) Surely this is self-evident. No-one ever recommends taking an important interaction out of a model because it's hard to present.
(2) Whatever kind of model you fit, you can still present its results in terms of categories if you think it will aid interpretation. Though ...
(3) You have to be careful to make sure it doesn't aid mis-interpretation, for the reasons given above.
(4) It's not in fact difficult to present non-linear responses. Personal opinion, clearly, & audiences differ; but I've never seen a graph of fitted response values versus predictor values puzzle someone just because it's curved. Interactions, logits, random effects, multicollinearity, ...—these are all much harder to explain.]
[An additional point brought up by @Roland is the exactness of the measurement of the predictors; he's suggesting, I think, that categorization may be appropriate when they're not especially precise. Common sense might suggest that you don't improve matters by re-stating them even less precisely, & common sense would be right:
MacCallum et al (2002), "On the Practice of Dichotomization of Quantitative Variables", Psychological Methods, 7, 1, pp17–19.]
