Is there any way to change the emoticons in the standard android sms app? The green robot smilies are incredibly irritating, IMO.

I'm open to suggestions of other SMS apps that have different emoticons as well, but the few I've looked at seem to just skin the standard SMS app, emoticons and all.
From what I've been able to glean - No, it's not possible via any built-in settings in the stock Messaging app.

Handcent SMS, however can disable all smiley icons so all you see is the actual text - the punctuation characters. To do this in handcent press MENU > SETTINGS > CUSTOM STYLE > BUBBLE SETTINGS

Move thru the list of options shown on the bottom (contained within a tab with an arrow) until you see DISABLE SMILEYS. Click that and when prompted SAVE your settings.