There have been several posts on the Adwords Help Forum recently detailing horror stories of inexperienced users being faced with large (sometimes huge) bills from Google after setting up their first campaign. In my opinion this is one of the key weaknesses of Adwords - that it's far too easy for the unwary to spend a lot of money with few results - but I do also acknowledge that it's difficult for Google to operate in any other way.
So, what can you do to avoid this scenario?
What I usually advise all my customers is that the 'first draft' of any new campaign is set up with a very low daily/monthly budget. Regardless of what you think you might spend eventually - even if it's thousands a day - I'd recommend that a new campaign is started with a monthly budget of no more than $100-$150. For the high cost clicks this won't get you many clicks a day, but for most keywords this should be enough to get at least one or two and it should also be enough to gauge the impressions achieved by your keywords and how costly your 'real' campaign will be. Most importantly, with this budget set you know that whatever happens, you won't be charged the earth overnight.
Don't forget that you can change your budget at any time so there's no downside to starting with such a low budget. Few businesses will be so desperate that they can't afford to wait at least a few days before the full budget is applied and I'd always argue that it's better to get it right than to throw money down the drain (especially if the business is desperate).
It's also important to always ensure your spend with Adwords is returning good results in the form of Return on Investment (ROI). Only you can determine what is a 'worthwhile' spend - and this may not always mean a positive ROI (where you earn more through Adwords advertising than you spend) but you are aware of the return and are happy with the costs before increasing your monthly budget. For example, supposing I set up a new campaign and set the daily budget at $4 (~ $120 a month). For this, my new campaign generates 10 clicks a day to my site that sells lawnmower spares.
Scenario 1: After a week and 70 clicks I haven't sold a single spare part via Adwords. Here there's absolutely no point in increasing the budget. Before I do anything I must try and work out why 70 visitors didn't buy a single thing; without any data, if I increase the budget I might get 700, or 7000 clicks without a sale (there might even be a fault on the website).
Scenario 2: After a week those 70 visitors resulted in two sales on different days, and I can reasonably suggest that I'll get a sale with every 35 clicks (roughly $14 spent on Adwords). At this point only I can work out if this is worthwhile. If the two sales totalled $100 then I might well be happy with this return and could increase the budget to $8 a day. After another week, if the sales are still 1 per 35 clicks I can increase at will, now fairly confident with that return. If the sales only totalled $40, then it's borderline and I should probably look at the site and would probably not want to increase the budget at this time.
Above all else, it's important to always think about what you're spending and whether it's returning good results. No one forces you to spend money with Adwords and no one except yourself is to blame if you spend too much without any return.