It seems that if you look back to not so long ago, everybody wanted to be an Empire. Russian Empire, Ottoman Empire, French Empire, British Empire, Empire of Japan, the list goes on.
Today I believe only Japan keeps the title. Is it because it's now seen as bad to have an empire? When did that change?
Not the answer but just to clarify, Japan has not kept the title of Empire of Japan. The formal/official name of Japan is State of Japan, Empire of Japan was dissolved after new constitution was introduced in 1947 after WW2, though the Emperor is still their head of state it is no longer an empire.
Assuming this is about the title itself, not monarchy in general.
For one thing, monarchies have become much less common, including in many of the countries you name. Russia, Turkey, and France no longer have monarchs of any sort.
The United Kingdom is a slightly different case. There is, of course, still a monarchy, but it only ever claimed one imperial title: Queen Victoria became "Empress of India" in 1876. The title lasted until India gained its independence; without it, there were no more imperial titles to be held.
More practically, the successor states no longer rule over empires in the usual sense. The term connotes rulership over many nations, rather than just one. The colonial-era empires (and their predecessors) were highlighting their conquests.
Japan is an exception: although despite the presence of an emperor, there is no empire. The country is known only as the "State of Japan" and the emperor lacks any constitutional power. Also, it's slightly more complex, since the title is "tenno," which is translated to mean "emperor" but literally means "heavenly sovereign," and of course, doesn't have the same derivation as European titles. I don't know if Japanese-speakers use the same word for European emperors.
Follow up question: does the demonifcation of imperialism have anything to do with nations dropping empire from their titles?