To a great degree you can do whatever you like provided you hold out enough data at random to test whatever model you come up with based on the retained data. A 50% split can be a good idea. Yes, you lose some ability to detect relationships, but what you gain is enormous; namely, the ability to replicate your work before it is published. No matter how sophisticated the statistical techniques you bring to bear, you will be shocked at how many "significant" predictors wind up being entirely useless when applied to the confirmation data.
Bear in mind, too, that "relevant" for prediction means more than a low p-value. That, after all, only means it's likely a relationship found in this particular dataset is not due to chance. For prediction it's actually more important to find the variables that exert substantial influence on the predictand (without over-fitting the model); that is, to find the variables that are likely to be "real" and, when varied throughout a reasonable range of values (not just the values that might occur in your sample!), cause the predictand to vary appreciably. When you have hold-out data to confirm a model, you can be more comfortable provisionally retaining marginally "significant" variables that might not have low p-values.
For these reasons (and building on chl's fine answer), although I have found stepwise models, AIC comparisons, and Bonferroni corrections quite useful (especially with hundreds or thousands of possible predictors in play), these should not be the sole determinants of which variables enter your model. Do not lose sight of the guidance afforded by theory, either: variables having strong theoretical justification to be in a model usually should be kept in, even when they are not significant, provided they do not create ill-conditioned equations (e.g., collinearity).
NB: After you have settled on a model and confirmed its usefulness with the hold-out data, it's fine to recombine the retained data with the hold-out data for final estimation. Thus, nothing is lost in terms of the precision with which you can estimate model coefficients.