My largest problem with the game (aside from the often blatant cheating--I even had a foot-tapping code with a couple of my friends) was that calling trump (the dominate suit) frequently relied on luck more than anything else. Unless I was directly to the left of the dealer, there was no guarantee that I could call the trump that I needed to be successful with my hand. This was particularly burdensome when I would have a "loner" hand only to have my partner call the opposite color.
I much preferred the game Hossenfeffer for this reason. It basically plays out like Euchre except all of the cards are dealt (there is no "kitty"), and instead of calling trump, the players bid for trump. This method of bidding falls comfortably in between the complexity of bidding in Bridge and the simplicity of bidding in the game Spades (although I've played Spades more often since Hossenfeffer is not as well known). The beauty of Hossenfeffer is that it keeps the core gameplay of Euchre while not punishing people as much for having a bad hand. It keeps the use of bowers (which can potentially give jacks a great deal of value) but also adds the "suits" of no-trump high and no-trump low (potentially giving nines and tens value).
Now there is still a chance that my partner might give a ridiculous bid that utterly negates my hand, but overall I certainly prefer bidding for trump rather than calling for trump.
What? Did you expect this post to be about something else?