Q: how can I make a large transformer less loud? I have a large 2600W 230V -> 28V transformer, and it makes a constant quite loud bzzzzzz sound while it works. Is there any way to make it more silent (other then buying an equivalent SMPS which I don't have money for now)?
I am looking for some quick and cheap ways to make it less loud. Wrapping the whole thing in a large towel might not be the best idea as it will probably prevent the transformer from cooling properly.
Why does it make that annoying sound anyway?

A: The explanation I've usually heard is 'loose laminations'; at least one of the laminations has room to vibrate with the time-varying magnetic field. 
Not sure what can be done about it. Some transformers have bolts through them to hold the laminations together, and it might be that tightening them would mitigate the buzzing somewhat. If there's an obvious gap somewhere, there might be some way to get some epoxy or something into the gap that would limit the freedom of movement of the adjacent laminations.

A: You might not be able to do much about the noise directly but you can always redirect the noise such that you hear less of it. 
Lower frequency noises are more difficult to absorb, they tend to travel right through the material. Thus wrapping a towel around it won't do much. They are however easily reflected by a dense hard material. 
Build a sturdy sound wall around one side and that should redirect the noise somewhere else while keeping good airflow to the transformer. 

A: Is the transformer mounted? If you temporarily unmount it, is it still noisy?  It could be that what it is mounted to is acting as a sounding board -- you might be able to use rubber insulators or otherwise modify the mount to reduce noisy generation.

A: I've used polyurethane on I large welder transformer. Typically they are coated a the factory with something similar. It just somtimes dries out with time. 
You can also put shims made from paper or wood between the coils and iron core.
After I coated mine I used it for an hour to warm it up and the vibration helped wick the poly into the laminations.

A: The sound is a result of the system creating large magnetic fields as a function of how it operates.  These fields are fluctuating, probably at 50Hz based on your input voltage but maybe 60Hz if your in the US.
These magnetic fields push and pull on components in the system, since perfect dampening isn't possible these components vibrate.  Some of what you hear isn't at 50/60Hz though, it is also harmonics of that frequency and interactions with other components.
You definitely shouldn't do anything that will limit air flow or otherwise create a situation where the transformer could overheat.  
You can poke around a bit (carefully) and see if you can find a particular components or panel that is vibrating and try to use something to dampen the vibration.  High Temp Dampening material may be an option.
That being said, transformers of that power are basically impossible to silence.  The transformer core or the windings are probably vibrating and causing most of the noise.  At high enough power levels the iron core itself actually stretches and contracts as well causing vibration.
Some designs try to isolate the core to prevent vibrations transferring to other components but its not something you can likely fix in an after-market fashion.     

A: Can't really help you with your problem, but I might be able to give you some insight into the cause:
Magnetostriction -- sounds cool, huh?

A: Get you some epoxy spray paint, open up the enclosure to get to the core and windings, and paint the heck out of it, pour it on thick, it don't have to be pretty, in fact you want runs, you want the paint to run in between everything the core laminates and windings. Put a fan on it for over night to dry it. 

A: If the transformer is so noisy that it cannot be effectively used, flooding the windings with epoxy paint can, in many instances, reduce emitted noise. Professional transformer makers will immerse an entire power transformer in epoxy. Yes, too much can reduce the heat dissipation, but to be sensible, if the transformer is running cool but noise, warm and quiet might be better.

A: From the factory, the transformer may or may not have been "conformal-dipped", meaning it was placed into a vat of liquid similar to polyurethane (but specifically designed for high temperatures and electronics work), then let to sit and dry. This helps "glue" everything together and prevent microscopic motion we perceive as "hum." The better transformers are dipped, then a vacuum pulled on it, releasing all the air bubbles trapped inside, allowing conformal into every nook and cranny. That works better, but obviously is more difficult and expensive. 
An alternative not mentioned yet would be mounting the transformer with rubber mounts into a sealed metal enclosure, filling it with a compatible transformer oil (or mineral oil), and using a liquid-cooling system. Many such transformers exist in electrical substations all over the world and are quieter and can handle more power due to liquid cooling.
