What should one do in London?

[PBI]

IMHO the British Museum is well worth seeing. 200 years of plundering antiquities from ancient civilizations has its perks, lots of interesting Assyrian, Egyptian and Greek stuff.

Otherwise I'd recommend the National Gallery if you're at all interested in art, and the Imperial War Museum. The former is on Trafalgar Square so has the advantage that you can just pop in while wandering around the main tourist bits, the latter however is out in the middle of nowhere on the south bank of the river and is quite a trip to reach.

The above three all have the added bonus that, last time I checked, they were all free admission (as I believe are most if not all the major museums in London).

Otherwise the Tate Modern has two reasons to visit:
1) The building itself (a former power station) is pretty impressive on the inside.
2) The cafe at the top is quite nice (and you can skip straight past the modern art to the top if you want).

Also, it's a nice walk from there along the river bank to parliament square, from which you can then easily get to Trafalgar Square via Pall Mall, thus seeing half the "famous" bits of London in one fell swoop.

The Science Museum and the Natural History museum are OK, though a little too "kiddy-friendly" for my tastes (though I do work in science, so a historian may well say the same thing about the British Museum).

I haven't been to the Tower in years, but IIRC it was expensive and crowded, though quite fun if you fancy something a bit less serious after all the highbrow art and ancient history.

Avoid the Underground at rush hour (though I suppose that applies to any major city), and I would recommend getting an Oyster card when you first use it, it's not any cheaper but makes getting the Tube a whole lot easier. Try not to have a heart attack when you see how much it costs for a cup of coffee anywhere in London. Be prepared to be molested and have your bag searched (and very likely be glared at by panicky-looking policemen with submachine guns) every time you enter anywhere.

I'm not quite sure why London seems so unpopular here, IMHO of the major cities I've visited London is as good as any, and a lot better than most. Certainly I can't think of anywhere where you can find as much interesting stuff to do for free.

[TinCow]

Anyone who says London isn't fun is insane. I lived there for 10 years and it's my favorite city in the world. As PBI said, the British Museum is excellent, but the Imperial War Museum is actually my favorite museum anywhere. It is a glorious place, with lots of fascinating stuff, excellent exhibits, and pleasant staff. If there's nice weather, I also highly recommend a stroll through Regents Park with a picnic lunch.

[Xipe Totec]

The British Museum is Paradise on Earth. It's always full of hotties, and has a great bookshop in the middle.

[Lemur]

Does the Groucho Club still exist?

And yes, as other posters have said, The British Museum is where they keep the loot of Empire. Very impressive.

[InsaneApache]

Anyone who says London isn't fun is insane.

You got me banged to rights there guv.