As my opinion, "no smoking is allowed" must be correct , because it's "passive voice" . Then I saw a title on 9gag.com that was "NO penguins allowed". So what grammar point is here?
A complete sentence would be "Penguins are not allowed" or its variation "No penguins are allowed".
However, on signs you can often find abbreviated sentences in which the verb is omitted (and often "be" can be implied). Common examples are "(there is) no entrance", "pedestrian crossing (is ahead)", "road (is) blocked".
A sign saying "no penguins" would be unusual (and possibly funny) due to its content, but its syntax is common.
No Smoking Allowed OR No Smoking is Allowed are BOTH wrong.
The sign should read: No Smoking or Smoking is not Permitted.
If "NO" Smoking is Allowed, what about smoking? The grammar is wrong (similar to a Double-Negative).