Tonight, December 20, 2010, there will be a full lunar eclipse visible from North America and many other areas. I recall there is a Gemara that says that a lunar eclipse is a bad omen for the Jews as the Jews are compared to the moon. By a rainbow it is mentioned not to show it to others as it is a bad sign due to the fact that Hashem would of destroyed the world. Is there any issur of looking or showing a lunar eclipse to others?
Rashi in Bereishis, chapter 1, Verse 14 on "והיו לאתת" mentions this issue of a bad omen from the eclipse. He says:
והיו לאותות: כשהמאורות לוקין סימן רע הוא לעולם, שנאמר (ירמיה י ב) מאותות השמים אל תחתו, בעשותכם רצון הקב"ה אין אתם צריכין לדאג מן הפורענות:
When there is an eclipse of the luminaries it is a bad sign for the world, as it is said: "Do not fear the signs from the heavens, etc." I.e., when you do the will of G-d, you need not worry about consequences.
Rashi appears to be clarifying the nature of what "signs" the verse is referring to. He states that the nation of Israel does not have to be concerned with the "bad sign" of an eclipse as the whole world considers it to be a bad sign.
Why does the world consider it to be a "bad sign"? Without wisdom and knowledge man tends to be primitive and superstitious. Primitive man attaches superstitious significance to the celestial bodies. Perhaps when the normative pattern is broken it shakes his sense of security and he anticipates a bad omen.
Why does the nation of Israel not need to be concerned? The nation of Israel when they keep the system of Torah properly operate based on a system of "חכמה", wisdom. Since they are operating based on wisdom they do not need to worry about a fear that comes from a superstitious reality. It will not affect them.
While researching another answer, I came across a comment by R' Yonasan Eibeschutz (in Yaaros Devash), that the Gemara's expression ליקוי חמה isn't referring to eclipses at all, but to sunspots.
(He doesn't seem to say what ליקוי לבנה might mean in this context. But I guess, according to his explanation, that it would also mean some kind of short-term phenomenon that reduces the moon's albedo - though I don't know what that might be.)
There is sicha of the Lubavitcher Rebbe on in his Likutei Sichos Vol. 15 on Bereshis explaining meaning of this Gemara. It does not mean that our influenced it but rather that force of Divine in the world is diminished and therefore it is to be and act as one should... go look it up..
Here's a link to an English translation of this Sicha from the book Mind Over Matter.