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For example, paper's structural integrity decreases when it comes into contact with a liquid. What happens at the time of contact?

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There are a great many descriptions of wetting action; you can read more here. If you are particularly interested in the wetting of paper, check out this question. If you have a more specific question, please clarify.

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I'm not sure that question mentions the change in structure of the paper, only what causes water to climb. Similarly the wikipedia article mentions what allows a surface to be wettened, but not structural effects. This doesn't really seem to address the question. – Jefromi Sep 13 '11 at 16:14
True, but the structural integrity was only provided as an example, it was not the focus of the question. The question was very broad and, IMHO, needs to be narrowed. – AdamRedwine Sep 13 '11 at 16:17

In the case of paper, fibers are connect to each other with hydrogen bonds. Water and humidity affect to these bonds and the fiber matrix loses its strength, or integrity.

In a more general way, water molecules tend to surround the charged particles (atoms, molecules) as they are polar.

Now, let these "charged particles" form the bonds of the material => water molecules surround them => particles bond with each other rather than other particles.

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