nkedel

Depending on where you go and with whom, phone:
- can coordinate with travel companions, without having to either spend 24/7 together (OK with my wife but nice to have the option to get away, gets old almost immediately with any of the buddies I occasionally travel with) /or/ spend time sitting and waiting at prearranged rendezvous.
- in urban settings, often quicker to call a cab than wait in a taxi rank or wait for one to pass to hail one (if safe at all; some places I've been it's generally considered unsafe)
- restaurant reservations
- check in with family/loved ones at home or be reachable by them in emergencies
- if you're single and unattached, I'm told it's sometimes useful if trying to pick up local company

Data:
- Maps!!! Seriously, this one is rarely that helpful on wifi, as it's when you're lost -- rather than at a cafe -- that it's most useful ... and I haven't yet found a really good offline mapping app for outside the US.
- Search for local amenities/restaurants/transit... yes, you can ask for recommendations, but if the choice is some guy recommending his brother-in-law's place vs. the crowdsourced wisdom of the internet, well, I know which one I'd bet.
- Translation -- yes, there are phrasebook apps, but the ability to pull up specific requests/instructions on Google translate is SWEET. Plus, in many cases, if you can get a local keyboard (or you're going someplace they use our alphabet), a lot of people can answer by typing into the phone.
- Check in at home more cheaply without using minutes (wifi works for this one, assuming your hotel has it and has a decent connection)

Depending on where you go, the answer is usually yet. Certainly on Bali proper.

I've not been, but basic GSM cell coverage is available in surprisingly rural places these days. I wouldn't bet on any kind of high speed data, of course.