What about generic lightning cables or adapters?
It's pretty much impossible to say for sure at the moment, as the cables aren't publicly available yet, nor are the licensing agreements, but we can do some informed speculation.

From a legal standpoint, if Apple is granted patents on the connector, they could go after anyone who produces a copy without a license. So far I haven't seen any evidence they've applied for a patent on it (nor can I find any about the original dock connector), but that doesn't mean it hasn't/won't happen. However it's a timely process, as a patent won't be granted right away, and litigation also takes time.

It's also worth considering that there seem to be a lot of no-name manufacturers producing dock connectors, and I suspect that while the numbers may be large in the aggregate, the individual ones are small enough that it may not be worthwhile for Apple to pursue all the small entities in court. They don't seem to have made a dent in the off-brand market for cheap 30-pin dock connectors, based on searching Amazon.

Apple can (and almost certainly will) license third parties to manufacture their own cables and connectors—they do this currently with the Made for iPod/iPhone/iPad programs. Anything that has the "MFi" logo on it is made by a company that has paid license fees to Apple:



From a technical standpoint, how difficult it is to produce depends on what's inside the connector exactly.

Apple has used various methods in the past to restrict certain dock connector features (mostly using some resistors in the connector I believe), but it's also possible that they'll use some active circuitry to prevent unlicensed copies. However I'd bet against that, as they have to make massive quantities of these, and the cost and production constraints of even a simple chip could make things problematic.

The physical connector is also unlike most other connectors out there (which come in all sorts of different sizes and shapes, but are largely made out of stamped metal with pins or an array of contact points). Everything on the Lightning connector is flush, and knowing Apple, the tolerances are probably fairly small. It may be different enough that it takes a while for other manufacturers to reproduce it consistently, but eventually I'm sure it's doable.

So my guess is that yes, we'll see cheap generic Lightning connectors, but it may take a bit longer, and the supply may ebb and flow if Apple takes legal action.