Step-down transformer that actually works?

Old question but I think the core of the right answer is still missing and since it's potentially a safety concern it may warrant another as answer.

1. All step down transformers are rated for a certain power. If you exceed the rated power, bad things will happen. YOU MUST NEVER EXCEED THE RATED POWER. A hair straightener needs a lot of power and would require a big and heavy transformer
2. Power rating is directly proportional to price, size and weight of the transformer. Hence there is a large variety out there. The first two hits on amazon are good example are this and this. The first one is small cheap and lightweight but handles only 200 W and the second one is big, bulky, expensive but handles 3000W. The one linked in the comments (mwave.com/mwave/SKUSearch.asp?px=FO&scriteria=AB05101) is BAD. It does not contain a power specification at all. From the looks of it, it would not work with a hair straightener.
3. The transformer must be configured properly: Most transformers can step down or up and need some adapters for the proper plugs at both ends. You have to make sure that input and output are set to the proper voltage (typically with switches on the product) and that you don't swap input and output accidentally

To answer the original question: You need to find find a transformer meets your power requirements and you need to configure it properly.

Hair straighteners are very power hungry devices and my guess is that either the power of the device exceeded the rated power of the transformer or that the transformer was configured improperly.

The problem is proper transformers tend to be heavy. If you had relocated to europe and wanted a permanent soloution to running american appliances I'd reccomend one of the "yellow brick" transformers they use on UK building sites. They are sturdilly built, are proper isolation transformers and have the power to run basically anything that comes with a normal domestic plug.

http://www.screwfix.com/p/portable-transformer-with-2-output-sockets-3kva/84144

Downside is they are bulky, heavy, expensive and you will have to change the plug on whatever you plug into them (I would suggest changing the plug on a power strip).

Products sold for travellers are at best likely to be autotransformers. Autotransformers will be about half the weight of isolation transformers but have two major downsides. Firstly they connect the output neutral to the input neutral which can cause problems if the supply is reverse polarity (see http://www.gson.org/stepdown/ ). Secondly they can fail in a way that leaves the input voltage on the ouput.

At worst products sold for travellers may not be transformers at all but instead may be triac based products. These reduce the RMS voltage but not the peak voltage. Fine for heating elements, very bad for anything else and probablly even more likely to fail in a bad way than an autotransformer.

Overall unless you need to travel with highly specialised equipment that simply can't be got in a 230V version or would be insanely expensive you are probablly better off simply buying universal or switchable voltage gear (universal being preferable to switchable but you don't often get the choice) and forgetting about the transformer.

You did not specify what kind of equipment, but in my experience most electronics I carry around can handle 100-240V on their own. (as @choster said) For old equipment you might well be able to buy a new adapter with the same specifications but also handles up to 240V.

However something nifty I found was a power-to-USB adapter. So I can charge my phone and mp3 player anywhere. Maybe this kind of solution can work for you. In my case I use some adapters from Skross.

As for good converter I think portability becomes a problem. (as @LorenPechtel said) You might try go to popular web shops and check what other consumers have to say.

I have a 2kW power converter from 240v => 120v that works well and weighs about 5kg - not suitable for holidays...

I have seen converters that use just a diode. This is very small and effectively chops the voltage in half with the disadvantage of a noisy signal. For something that is just a heating element (e.g. a simple kettle) that works fine. For anything with a motor or electronics, it probably won't.

A hairdryer has both a motor and a heater, so this probably won't do it. A hair straightener is mostly a heater, but they may well have electronics, and that won't work.