I actually worked on HVDC schemes, back in the mid-to-late 90s. Olin Lathrop's answer is partially right, but not quite. I'll try not to repeat too much of his answer, but I'll clear up a few things.
The losses for AC primarily come down to the inductance of the cable. This creates reactance for AC power transmission. A common misconception (repeated by Olin) is that this is due to transferring power to things around it. It isn't - a coil of wire halfway between here and the Magellanic Cloud will have precisely the same reactance and cause precisely the same electrical effects sat on your desk. For this reason, it's called self-inductance, and the self-inductance of a long transmission cable is really significant.
The cable does not lose any significant power from inductive coupling with other metalwork - this is the other half of that common misconception. The effectiveness of inductive coupling is a function of the AC frequency and the distance between the cables. For AC transmission at 50/60Hz, the frequency is so low that inductive coupling at any kind of distance is utterly ineffective; and unless you want to get electrocuted, those distances have to be several metres apart. This just does not happen to any measurable extent.
(Edited to add one thing I forgot) For cables running underwater, there are also very high cable capacitances due to their construction. This is a different source of reactive losses, but is significant in the same way. These may be the dominant cause of losses in underwater cables.
Skin effect does cause higher resistance for AC power transmission, as Olin says. In practise though, the need for flexible cables makes this less of an issue. A single cable thick enough to transmit significant power would generally be too inflexible and unwieldy to hang from a pylon, so transmission cables are assembled from a bundle of wires held apart with spacers. We'd need to do this anyway, whether we were using DC or AC. The result of this though is to put the wires within the skin effect zone for the bundle. Clearly there is engineering involved in this, and there will still be some losses, but by this happy coincidence we can make sure they're a lot lower.
Buried and submarine cables are a single thick cable, of course, so in principle they could still get bitten by the skin effect. Heavy-duty cable construction though will generally use a strong central core which provides structural integrity for the cable, with other connectors wound onto that core. Again, we can use that to our advantage to reduce skin effect in AC, and even HVDC cables will be built the same way.
The big win in power transmission though is eliminating reactive losses.
As Olin says, there is also an issue with joining two power grids together, because they will never be exactly the same frequency and phase. Clever use of filters in the mid-20th century did allow connection of grids, but designing these was as much art as science, and they were inherently inefficient. Once you've got your power transmitted in DC though, you can reconstruct AC with the exact same frequency and phase as the destination grid, and avoid the problem.
Not only that, but it is much more efficient to convert from AC to DC and back to AC again, instead of trying to use filters to compensate for phase and frequency. Grids these days are commonly joined with back-to-back schemes. These are essentially both halves of an HVDC link next to each other, with an enormous busbar between the two instead of kilometres of transmission cable.