Internet companies may launch their initial public offerings of stock with a splash, but that public arena has its drawbacks as both Facebook and Zynga are learning.

Zynga Inc., the maker of Facebook’s most popular games, Farmville, Words with Friends, Draw Something and others, saw it shares fall sharply yesterday on the heels of a report from analysts at Cowen and Co. saying the number of active daily users of its games fell 8 percent in May.

That’s the second consecutive monthly drop. All the Zynga games declined.

The San Francisco-based company’s stock fell 10 percent to $4.98 yesterday afternoon, down more than 50 percent from its $10 IPO price. The stock has traded as high as $15.91 (March).

I don’t know about you, but I’ve been seeing a decline in Zynga game-players on my Facebook  stream for quite a while. While the games were extremely popular, many Facebook users did not like all Farmville and other game requests popping up on their newsfeed if they didn’t play.

Cowen and Co. analyst Doug Creutz said consumers are switching to mobile games, something Zynga has been experimenting with, although the Facebook games are still its major focus.

Creutz said that Zynga’s games trail more weighty role-playing and multi-player games on mobile phones.

We’re not sure we agree with that. We see people playing easy zombie shooter games, Angry Birds, and solitaire most often on mobile devices.

What do you think? Are Facebook games a dying fad? Would you be sorry if they were?

Creutz cited figures from AppData in his analysis. — Allan Maurer