Can speakers of Mandarin Chinese and Cantonese understand each other?

No, they can't.

However, they can read what each other writes. The grammar is exactly the same--but the sounds for characters are sometimes wildly different. As an example, Peking and Beijing are the same city. "Peking" is not a bad transcription of what somebody would have said in the port of Canton (speaking Cantonese), but it's a TERRIBLE transcription of what somebody in Beijing would have said (speaking Mandarin)!

Chinese state TV broadcasts almost all of its shows with subtitles. It's funny because almost all the people watching TV speak "Chinese"... but if the program is in Mandarin, then the Cantonese speakers definitely can't understand it without the subtitles.

They can understand each other just fine if they write to each other, however, so don't forget that it isn't like they can't communicate (if they are literate).

I'm Cantonese and cannot understand Mandarin as it was never spoken in the house hold where I grew up. Plus before 1997 in Hong Kong, nearly all Chinese citizens all spoke in Cantonese, films were in Cantonese etc. The only Chinese back then that spoke Mandarin where from China's mainland who had come into Hong Kong illegally. The slightly older generation understand, but I wouldn't say a 100%. Hong Kong now has citizens that speak both Cantonese and Mandarin so future generations will be more fluent. The programmes and news are now mostly in Mandarin, but there are still Cantonese films and programmes for the viewing public.
It's rather like saying the Welsh can speak both languages but other UK nationals can only speak English, this is because there is no need for us to learn Welsh as its not used anywhere else in the world other than in Wales.
I would say the same for Mandarin Chinese having difficulty understanding Cantonese, the dialects are very different and you'd have to listen and concentrate hard to pick up certain words that sound alike. Forgot to mention that I was born and brought up in the UK, lived in Hong Kong as a child for a couple of years.

Simple answer: no!

Many people might dispute this but only because they're used to hearing the other dialect or because they think they "know" the other dialect by knowing a just few phrases. Ask any pure Cantonese or Mandarin speaker with absolutely no knowledge of the other dialect if they can converse with the other and I can guarantee you (and even bet a million dollars on it!) the answer is NO!

No, because the sounds of each dialect are very different.

For example, the phrase "going to school", spoken by Mandarin Chinese it's "shang xue" but spoken by a Cantonese it's "fan hok".

If you want to test it out, say something in Cantonese to a person from Taiwan (they speak Mandarin), and you'll know.

No. Not generally. They are completely different languages. Even speakers of different versions of Mandarin or Cantonese might not understand one another.

However, they all use the same writing system, so they can understand one another through reading and writing, but not speaking. This is why, if you ever watch Chinese programmes on television, you will see subtitles at the bottom of the screen - so that people from different regions of China can understand even if they cannot understand what is being said.

I'm learning some Chinese in martial arts. The two languages have some similar words, but many are totally different. Speakers of these two dialects can't understand each other very well. Here are some surnames in Mandarin & Cantonese.
Chang & Cheung
Wang & Wong
Lee & Lei
Wu & Eng
Wu & Mo
Chu & Jee
As you see, some words may be recognizable, but others are too different to recognize.

The Cantonese speakers can understand the Mandarin,but the Mandarin speakers don't always understand Cantonese.

I'm living in Guangzhou city of China where all of the local people speak Cantonese. By and large, Mandarin speakers are not likely to understand Cantonese speakers because Cantonese is way diifferent from Mandarin in pronunciation. However, Cantonese speakers can easily understand Mandarin because Mandarin has been imperative in Chinese school education the last decade. Every local person (except those too old people) is able to understand Mandarin now. Here are thousands of Guangzhou people I found online: http://www.hellochina.com/u/10751 you may talk with them in Mandarin and I bet they will surely understand you.

Traditionally, there are seven dialect groups in China, which are not always mutually comprehensible. In other words, speakers of Mandarin Chinese and Cantonese don't necessarily understand each other -- although Mandarin is the official spoken language and chances of Cantonese speakers understand it are much higher.

This depends on your definition of understand.

I grew up speaking Cantonese and I DO understand Mandarin Chinese. If I hear someone speaking it, I can comprehend what they're saying and its meaning. Speaking though, is different. Since it's a different language, I have to learn the different ways to the language's pronunciation. My pronunciation is not great, it's good enough to be understood by learners and natives of the language. Some Mandarin speaking people CAN understand Cantonese, but others do not. Likewise, I'm one of the Cantonese speakers who understand Mandarin, but that does not mean that all Cantonese speakers can understand Mandarin.

Some Cantonese and Mandarin speakers can't understand the other's language when spoken at a fluent rate, but when slowed down... they can make out the general meaning. This is because Cantonese and Mandarin are what I like to call "Cousin Languages" meaning they are similar, but different enough to be two separate languages.

And of course, there are some people from both language worlds who completely do not see the similarities between the languages and cannot understand the opposite languages at all.