How does power affect soldering irons? Is 30 Watts enough?

Wikipedia is pretty good on the Soldering iron.

Does your soldering iron look like this simple soldering iron just an iron and mains cable:

Or more like this soldering station where the iron plugs into a box, which is a transformer or controller:

I would expect a 30 watt iron to look like the 'simple soldering iron', maybe even slimmer. Their temperature is usually not controlled (unless it is made by Weller).

A 30 watt 'simple soldering iron' is okay for modest electronics. Soldering ordinary through hole electronic components and thin (e.g. mm) wire, even the thin metal legs on DC power plugs and sockets, should be fine.

A simple iron relies on thermal equilibrium to maintain its temperature. It loses as much energy as put in by the heating element. Hence it's tip temperature will vary when it is used. This is okay. You could solder many solder joints, providing the iron has time to recover and reach working temperature, i.e. you are in no particular hurry.

As the other two answers state, large parts need a lot of energy to heat the part and melt solder. Soldering with an underpowered iron might damage plastic or glue around a part, and may produce a poor soldered joint. As a more extreme example, it would be hard to solder a battery lead for a car battery with a 30 watt iron, because the heat would be conducted away too rapidly for the soldering iron to heat it up.

Larger wattage irons are either big and designed for heavier jobs (for example soldering leaded windows :-), or they are temperature controller to maintain tip temperature.

The advantage of a higher power temperature-controlled soldering iron is it maintains a relatively constant soldering temperature even while it is being used. That is very important on a production line, or where a lot of soldering joints need to be made relatively rapidly. A 'simple iron' is likely to drop too far below adequate soldering temperature, and slow the operator down; no problem for a hobbyist, but time and money for a manufacturer.

A temperature controlled iron is usually much higher power than a 'simple iron', for example 80W or more. This allows it to maintain a working temperature while it is being used, and heat parts with larger thermal conduction or capacity. It won't slow down an operator, and is a bit more flexible on what it can be used for than a 'simple iron'.

I prefer to use a temperature controlled iron when I teach beginners to solder because it is consistent. I think they can get a 'feel' for soldering more quickly than by using a 'simple iron'. Once a person has some confidence for soldering, it is easier to adapt to a less consistent soldering iron. They know when it is the iron or their technique which is making poor solder joints.

I don't think it is worth spending a significant premium to get a good temperature controlled iron unless you plan on using it frequently. I have tried a modest price temperature controlled iron (discount from £60 to under £35). It was noticeably better than the other cheaper irons I have used. It's only disadvantage was the soldering tips came in packs of three, and only one seemed useful. A professional product might have dozens of tips which may enable it to be used successfully in more situations.

A low-cost investment which I like is a brass-wool 'sponge' soldering tip cleaner.

This cleans the tip just as well as the usual 'damp sponge', and has less effect on the tip temperature than a damp sponge. So I think it helps improve the usefulness of simple irons.

I'd also recommend a soldering stand for the iron, so that it is always easy to pick up, and doesn't roll across a workbench.

If you were a control system, and you saw your iron was only at 150 degrees, and you wanted to try REALLY HARD to get that temperature up to 330 degrees Celsius by cranking up the current to the heating element.. But what if you were trying as hard as you can (no more current source left) but the temperature still will not go higher?

The reason is because there is literally not enough power left to overcome whatever heat sinking is happening to the soldering iron (perhaps you are trying to solder a huge piece of metal, or a large battery terminal?) and the iron cannot reach the intended temperature.

Low quality iron control systems will just fail horribly, especially if they are open loop. The better quality ones with temperature control feedback will obviously not have enough available current, despite attempting to reach the required temperature, so again they will fail.

If you have an open loop poor quality iron and try to solder onto a large heat sink, it will probably NOT reach the proper temperature, because it doesnt KNOW that the iron tip is not actually reaching the intended temperature for the given power input to the system.

The good quality irons with temperature control AND a high power rating WILL be able to compensate for the target's heat sinking ability and crank up the current until indeed the iron tip reaches the correct temperature.

The power rating of a soldering iron/station also helps the control system with the "rise time", or the time taken to reach the temperature set point, by effectively giving the system more 'gain' and therefore it's response to changes in temperature are also much better. A good example of this is the time taken to reach the set temperature from a cold start will be very short for a good quality, high power iron, compared to a low power or poorly controlled iron.

I hope that helps - my explanation involves a bit of metaphor and similes to classical control systems, I hope you understand the references.

When talking about the wattage of a soldering iron and whether it is sufficient or not one really has to distinguish between unregulated and regulated tools.

Unregulated soldering irons usually have a fixed wattage that is selected to fit the given size of the tool tip. For electrical and electronics works and small to medium sized tools (say less than about 2 mm width) 30 W should be sufficient. Issues arise when soldering large or highly thermal conductive components due to decreasing temperature of the tool tip.

Regulated soldering (aka temperature regulated) irons are already covered by KyranF's answer. High power ratings mean in that case the ability of the tool to reach the desired temperature fast (e.g. coming from stand-by temperature or during soldering of components) as well as the ability to solder components with a large thermal mass (e.g. ground planes or heat sinks) while maintaining the pre-set temperature.