Should I have a spare cassette or a spare wheel? I have a road bike that I use for triathlons as well as club rides in the evenings and on weekends. I don't have the bike in front of me, but the range of the cassette is on the low side. I'm more likely to run out of gears going uphill than down.

I'm going on a bike trip in the Alps next month and it'd probably be to my advantage to have a bit more breathing room for climbing if I'm going to be doing it an entire week. That's why I'm considering getting another cassette with a wider range. Does it make more sense to have a separate cassette that I swap onto my current wheel when needed or should I go ahead and get another wheel to make the swap easier. I don't necessarily want to take apart wheel each time I want to swap. How do people usually handle this?
It's a personal choice. If you're going to run the same tires, then just go with a spare cassette. It's pretty easy to swap them out, so I don't see that as a big deal. However, If you're going to have different tires and a different cassette, then I'd probably opt for the different wheelset. If you need a more durable wheelset for touring, you might also consider a separate wheelset.  

I tend to have a road and off-road set of tires for my cross bike. Since it's a lot more work to switch the tires each time I want to ride different types of terrain (and want a slightly larger range on the off road set), I prefer to have a separate wheelset.

It only takes a minute or two to swap a cassette, and also gives you time to get the other one good and clean while it's off the bike.