The convolution operation is defined by this flip, e.g. for 1D
$$(f * g )(t)\ \stackrel{\mathrm{def}}{=} \int_{-\infty}^\infty f(\tau)\, g(t-\tau)\, d\tau$$
If there was no flipping it would be called cross-correlation, in 1D this is
$$(f \star g)(t)\ \stackrel{\mathrm{def}}{=} \int_{-\infty}^{\infty} f^*(\tau)\ g(t+\tau)\,d\tau$$
You don't have to do the flipping if the resulting kernel is no different, e.g. an isometric filter.
One reason convolution is used instead of cross-correlation is that convolution is a simple multiplication in the fourier domain, e.g. from wikipedia
$$\mathcal{F}\{f * g\} = k\cdot \mathcal{F}\{f\}\cdot \mathcal{F}\{g\}$$
where $k$ is a constant depending on the normalisation constant of the Fourier transform used.
Proof can be found on wikipedia here:
http://en.wikipedia.org/wiki/Convolution_theorem
Cross-correlation (no flipping) can also be done in the Fourier domain, e.g.
$$\mathcal{F}\{f\star g\}=(\mathcal{F}\{f\})^* \cdot \mathcal{F}\{g\}$$
where $(\mathcal{F}\{f\})^*$ is the complex conjugate of $\mathcal{F}\{f\}$
Another nice property of convolution is that the operation is commutative, e.g.
$$f(x) * g(x) = g(x) * f(x)$$
whereas for cross-correlation it is not.
Even nicer is that convolution of a signal with a dirac delta returns the original signal, shifted, where as for cross-correlation a flipped, shifted, signal is returned.
More information on wikipedia here:
http://en.wikipedia.org/wiki/Cross-correlation
Although it is just a simple flip, convolution and cross-correlation can give quite different results, e.g.:

(note that change in y axes range). The cross-correlation result has a peak exactly at the centre where the two unflipped functions match. Normalised cross-correlation is often used for template matching. The convolution result is different.
See also:
https://dsp.stackexchange.com/questions/2654/what-is-the-difference-between-convolution-and-cross-correlation
The mathematicians take: https://math.stackexchange.com/questions/353272/whats-the-difference-between-convolution-and-crosscorrelation