Nope! Here's a list of words with the same singular and plural form.

Most are either animals (deer, moose, swine, etc.) or relatively new words (aircraft, hovercraft, etc). Most of the animal names ultimately come from a root that is neither Latin or Greek (you can use this online etymology dictionary to see for yourself), which makes sense because Latin and Greek nouns typically were very regular in how their forms were declined.

I only know of a few irregular nouns in Latin. This article on the plural of virus sums it up well:

The crucial problem here is that, classically speaking, there appears to be no recorded use of virus in the plural. It was a 2nd declension noun ending in -us, which is rather common, but it was also a neuter, which is rather rare. I could only come up with three such 2nd declension neuters: virus (some poison), pelagus (the sea, usually poetically), and vulgus (the crowd). None appear to admit plurals. Perhaps this is because they are mass nouns, not count nouns.

So basically, Latin nouns had very specific rules for whether something was singular or plural. This is incredibly important because Latin has a very different syntax than English does. Word order was actually relatively unimportant because it was the word endings that gave the word's meaning in the sentence and not the context.

For example, the sentences

canis edit canem

canem canis edit

edit canis canem

etc.

all mean

dog eat dog

The different endings on the noun root word (canis) define whether it is the subject (canis), direct object (canem), etc. as well as whether or not it is singular or plural.

Another thing you can take away from this is that the plural of virus is not "viri" or (shudders) "virii." Instead it likely lacked a plural because its use and meaning in its original language differs from how it is used and defined today. So the proper plural of virus would be the English tradition: viruses.

tl;dr etymology (the history of words) is pretty neat, and penis >> penises/penes, virus >> viruses.