I'm going to fly from the UK to Canada via EWR (Newark Liberty International Airport). Do I need to apply for a Visa Waiver through the ESTA (Electronic System for Travel Authorization)?
Yes, you do need one.
The US doesn't share the concept of "in international transit" that a lot of other countries have. When you step off a plane on US soil[*], you must clear US customs and immigration. Only then can you proceed to board your next flight.
The DHS have an entry about this in their FAQ:
Do nationals or citizens of countries that participate in the Visa Waiver Program require travel authorization if they are only transiting the United States in route to another country?
Eligible nationals or citizens of countries that participate in the Visa Waiver Program require either a travel authorization or a visa to transit the United States. If a traveler is only planning to transit through the United States en route to another country, when he or she completes the travel authorization application in ESTA, the traveler should enter the words "In Transit" and his or her final destination location in the address lines in the Address While In The United States field on the application.
[*] In a few places (such as Canada an Ireland), they have juxtaposed border controls and you end up clearing US customs and immigration before boarding the plane. Either way, you still need to clear immigration on an international connection.
Yes you do. There's no concept of 'transit' in the US. The good news with the Visa Waiver Program, however, is that you only have to go through it once and then it's valid for two years - so if you go through again in that time you just present the same number.
It's fairly easy to do, provided their system is online (took 2 days before I could pay on it!).
There's still something weird about paying for a visa waiver though, feels suspiciously like a visa to me ;)