cross pollination of sweetcorn is a risk because they are wind pollinated - the male flower is at the top, the female flower half way down the stem, the wind transfers the pollen.
Its less of a worry with insect pollinated plants. Im not exactly sure why.
in answer to sausage's question, and assuming no prior knowledge of such things-
When cross pollination occurs, genetic traits of each parent variety are transferred. These may be recessive and cause no problem, or may be dominant traits and alter the nature of the resulting plant. This is exactly what is done, under controlled conditions, to create hybrid varieties. If a hybrid variety (an F1 say) cross pollinates with a lesser variety, the advantages that the hybrid has can be lost. As mentioned this is of most worry if you are saving seeds for the next generation of plant, but can also cause abnormalities in the seeds or fruit that are noticable if that is the part of the plant that is desired, as it is in the case of maize (sweetcorn). There are many examples on the internet of the effects on the cobs of cross pollination, and in fact maize cobs were used as the example in my studies, of the effects of genetic alterations.
Of course the most famous example of cross pollination effects are the studies carried out by Gregor Mendel on pea plants, which led to our knowledge of hereditry.
If you think about it, you are a specific variety of your species (homo sapiens sapiens for most of you), and your partner (im assuming a F/M sexual partnership here. No disrespect to anyone intended but its the only type that works for hereditry studies) is another specific variety. If you have a child, you are effectively cross-pollinating your variety (from your parents genes) with your partners, the result is that your offspring share genetic traits with you both. Some may increase desirable factors, for instance my son seems to have perfect vision, which may be a cancellation of the trait both me and my wife have of short sight. Other variations can result in genetic disorders. Exactly the same occurs in plants. Specially bred hybrids will have very desirable characteristics (my F1 sweetcorn for example has been developed for increased sugar content) that can be cancelled by cross-pollination with a lower variety.
hope thats sufficiently simple for you. Not exactly an easy subject genetics!
(and of course hoping thats what you wanted to know, and your still awake
)