Which airlines will cancel the return leg of a flight if you do not use the outward portion?

Instead of giving a list of airlines, I’ll give a few pointers which can help find out.

The reason airlines cancel subsequent segments of a missed flight is to avoid passengers taking advantage of hidden-city ticketing (where a flight A-B-C is often cheaper than A-B or B-C) or abusing cheap round-trip fares with attached conditions (staying at the destination a minimum amount of time or over the week-end, for instance), which cost a lot less then two separate one-way flights.

For the former, it implies the airline selling connecting flights (usually through one of their hubs). For the latter, it implies airlines which have return fares.

Both are the traditional model of the incumbents (former flag carriers) and other “full service” airlines.

On the contrary, most low cost carriers usually have a much simpler model: each flight is independent. No connections, and no discounts for return trips. You can book the two segments separately, it will usually be exactly the same price as the return flight (there may be a small difference due to taxes and/or local currencies, but it will be quite symbolic.

So those airlines, like Vueling or Ryanair in your question, do not care if you miss a flight. You paid for it whether you did or did not fly, and it doesn’t matter if you don’t.

On the other hand, full service airlines do have an interest in preventing you from “abusing” their “cheap” fares, and are a lot more likely to cancel subsequent flights. Note that this may vary depending on the fare paid: fully flexible fares usually won’t have these policies applied (since there’s no “discount”), but of course reading the fine print is essential.

There are certainly exceptions here or there (and there are airlines which are difficult to classify), but that’s the essence of it.