Recently I purchased an external battery for my Thinkpad. The internal batteries were getting weaker, and I also needed something for the 14 hour overseas flights. I picked up a generic one on eBay, a 17 volt battery with about 110 watt-hours, for about $120. It's very small, and only about 1.5 lbs. Very impressive for the money. (When these things first came out they had half the capacity and cost more like $300.)
There are downsides to an external: The laptop doesn't know how much charge is in the battery and doesn't charge it. You need an external charger. My battery came with its own very tiny charger which is quite slow (it takes almost a day to recharge from a full discharge.) The battery has its own basic guage built in, however. An external is not as efficient as an internal (you convert the 17v to the laptop's internal voltage and you also do wasteful charging of the laptop's internal if it is not full, though you can remove the internal at the risk of a sudden cutoff should you get to the end of the external's life.)
However, the plus is around 9 to 10 hours of life in a small, cheap package, plus the life of your laptop's internal battery. About all you need for any flight or long day's work.
It's so nice that in fact I think it's a meaningful alternative to the power jacks found on some airlines, usually only in business class. I bought an airline adapter a few years ago for a similar price to this battery, and even when I have flown in business class, half the time the power jack has not been working properly. Some airlines have power in coach but it's rare. And it costs a lot of money for the airlines to fit these 80 watt jacks in lots of seat, especially with all the safety regs on airlines.
I think it might make more sense for airlines to just offer these sorts of batteries, either free or for a cheap rental fee. Cheaper for them and for passengers than the power jacks. (Admittedly the airline adapter I bought has seen much more use as a car and RV adapter.) Of course they do need to offer a few different voltages (most laptops can take a range) but passengers could reserve a battery with their flight reservation to be sure they get the right one.
It would be even cheaper for airlines to offer sealed lead-acid batteries. You can buy (not rent) an SLA with over 200 watt-hours (more than you need for any flight) for under $20! The downside is they are very heavy (17lbs) but if you only have to carry it onto the plane from the gate this may not be a giant barrier.
Of course, what would be great would be a standard power plug on laptops for external batteries, where the laptop could use the power directly, and measure and charge the external. Right now the battery is the first part to fail in a laptop, and as such you want to replace batteries at different times from laptops. This new external should last me into my next laptop if it is a similar voltage.