The Kothel Hamma'arabi (Western Wall) is the only remnant that has remained for us, of the destruction of the Beth Hammiqdash (Temple). The holy Zohar tells us that the Shechinah (G-d's holy Presence) has not departed from it.
The Kothel Hama'arabi (Western Wall) must, therefore, be treated with the utmost respect. We are not permitted to destroy the smallest portion of it (hammering a nail into it would be forbidden) or treat it in an undignified manner. Nowadays the Kothel is well lit with electric lighting, but in the days when people only had candles, there were some people who would place a candle on the wall for light. This is forbidden because it blackens the wall, in addition to the fact that we may not use the wall for any purpose.
Apparently, some people would also write their names on the stone of the Kothel itself, and this was forbidden for the same reason. Today, the authorities would be quick to prevent people from writing on the Kothel or defacing it in any manner, however, we must be particular to behave appropriately there, not only because it is a remnant of the Beth Hammiqdash, but especially since the Shekhinah is present.
(See Kaf Hahaim 151, Oth 76)
