Like MoiraWendy, I use 'whom' where it is needed,  particularly in writing.

This is because there are some situations where you have no choice but to use 'whom', such as in the middle of a sentence following a preposition. I sometimes also use it in speech, especially in relatively formal contexts.

But, yes, it's true. There are millions of native English speakers who never use 'whom'. And there are also millions of native English speakers who say 'you was' and 'he don't' every day of their lives. This doesn't mean you have to follow their example!

I still use whom as required; "to whom" makes sense, "to who" is the noise an owl makes.

But English is a live language and things keep changing.  The funny one for me is when people don't know when to use "I" and when to use "me", so they think they are avoiding the problem by using "myself", which is just funny.  After all why use 6 letters when 1 or 2 will do?

Even funnier is listening to Labour party politicians who have been educated correctly.  They get to the place where "I" should go and pause, then put in "me" because they think it is more socially correct.  It is as if the Fabian society never existed. :-)

A continuing debate in English usage is the question of when to use who and when to use whom. According to formal grammar, who forms the subjective case and so should be used in subject position in a sentence, as in who decided this? The form whom, on the other hand, forms the objective case and so should be used in object position in a sentence, as in whom do you think we should support?; to whom do you wish to speak? Although there are some speakers who still use who and whom according to the rules of formal grammar as stated here, there are many more who rarely use whom at all; its use has retreated steadily and is now largely restricted to formal contexts. The normal practice in modern English is to use who instead of whom (and, where applicable, to put the preposition at the end of the sentence): who do you wish to speak to?; who do you think we should support? Such uses are today broadly accepted in standard English.

I agree with other commenters here.  There is one situation in formal writing I can think of where you must use it.  

e.g. "London is home to people from all over the world, many of whom speak English as a second language."

When you need to use a preposition, you always need "whom" - it would look and sound strange if you didn't use "whom" and would very definitely be a mistake.