How to fly on the new Boeing 787 Dreamliner?

This is a list of airlines that have ordered a Boeing 787. So I would look at their flight planes to maximize your chances:

ILFC1 67

All Nippon Airways 40

Air Canada 37

Japan Airlines 35

Vietnam Airline

Qatar Airways 30

Qantas Airways 35

Etihad Airways 31

Singapore Airlines 20

British Airways 16

Virgin Atlantic Airways 15

The Jan 2013 spate of Dreamliner problems has led to news articles that include stats about fleet size.

For example, from CBC news,

• All Nippon Airways has 17 Dreamliners
• The two Japanese carriers have just over half of all 787s that are currently flying
• Air Canada has 37 firm orders for the planes, to be delivered in 2014

And from Yoimuri,

• ANA has 17 of the aircraft in its fleet and Japan Airlines has seven, accounting for almost half of about 50 787s in service worldwide.

(I am not clear why 24 can be "over half" and "almost half" of 50 at the same time)

This Guardian article goes with the same "almost half" factoid and adds,

• British Airways, Thomson and Virgin have placed orders, with BA expecting to operate the first of its 24 Dreamliners this year.
• LOT (which is Polish) has 2 and is doing Chicago-Wroclaw with one of them

Read enough of those articles, though, and you'll probably be in a little less of a hurry to get a chance to fly one.

New articles as the grounding continues.

This CTV News coverage,

• Ethiopia Airlines: 4 (Washington D.C. to Addis Ababa -- a distance of 11,500 kilometres and the airline's longest-ever flight)
• Poland's LOT is the only European airline flying Dreamliners: 2
• United Airlines is the only US airline flying Dreamliners: 6
• Japan's ANA: 17
• Japan Airlines: 7
• Air India: 6
• Chile's LAN Airlines: 3
• "That accounts for 45 of the 50 Dreamliners Boeing has shipped since the first one was delivered to ANA in 2011"

May 2013 coverage of the return to flight reveals more.

A CNN article says 8 airlines fly it:

• Qatar Airways (Doha - Dubai, Doha-Heathrow) - and this is the one we didn't know about before so presumably they have 5
• Ethiopian Airlines (Addis Ababa-Nairobi)
• ANA
• Japan Airlines (and the same factoid that ANA and Japan Airlines have 24 of the 50)
• United (Houston - Denver)
• LOT
• Air India
• LAN

Some are starting flights in May, others in June. The routes they are using do not, in general, seem like the routes this plane is needed for, so expect schedules to continue to adjust.

I read on the airliners forum that Frankfurt-Tokyo could be an option starting in january. There are many suggestions on this forum. Since most of the visitors to this forum appear to work in the airline industry, I would consider this info trustwordy.

You can find other suggestions on this forum thread as well.

Ben Schlappig (Lucky) at the One Mile At A Time blog has posted a few times about award availability on 787 flights. This search should turn up the relevant posts.

His recommendations for flights to look for are Tokyo Haneda to/from Frankfurt from January on ANA, or a little further in the future, Tokyo to/from Boston from late April on JAL.

If you are in the UK, Thomson Airways which is the British arm of their German parent travel company TUI in Summer 2013, will be the first UK airline to get the state-of-the-art 787 Dreamliner. You’ll be able to fly on the Thomson Airways 787 Dreamliner on certain flights to Florida and Mexico from Gatwick, Manchester, East Midlands and Glasgow airports.

The first long haul flight of the Thomson 787 Dreamliner has been given the green light for the second week of July. Passengers heading to Cancun and Florida from July 8th will be the first to fly long haul on the state-of-the-art jet.

You can read much more inc. videos about Thomson's new super jet here

Update:

The Scandinavian Airlines - Norwegian has announced its Boeing 787 Dreamliner will be used on flights between London and Oslo this summer 2013. The carrier will deploy the aircraft on the route on Thursdays and Sundays between 4 July and 4 August. The aircraft will also be used on other routes from Oslo to Malaga, Alicante, Barcelona and Nice.

Norwegian currently has eight Dreamliners on order with three to be delivered this year, four in 2014 and one in 2015.

More information about Norwegian's new 787 Dreamliner can be seen here.

United Airlines has begun operating the 787-8, initially on certain domestic flights to and from Houston (IAH). One way to find them is by searching their PDF timetable for the string "788".

A simple way is to search by aircraft type at flightaware. The 787 is called 788/9 for flight planning, so a quick search leads to a nice timetable and map of flights: