What’s the right term for "expensive things that have no real use"

A white elephant is expensive but useless.

Trinkets is a good word for this. Baubles is also good. The phrase status symbols might also work, but it would only imply "expensive" not necessarily "no real use".

I think the term you may be looking for is positional good, which is the economist's term for things bought chiefly to prove you can afford them, rather than for any real use.

See also here.

I agree 100% with onomatomaniak. Avoid trinkets, baubles and trifles as they all imply that the items are cheap. I also agree with onomatomaniak's suggestion to use the term "luxuries". You could also go with the very similar term of "luxury items".

Another term which you might consider (and which I quite like myself) is "extravagances". Oxford Dictionaries Online defines the terms as "a thing on which too much money has been spent or which has used up too many resources". An nice example sentence (from Urban Dictionary) would be "Nouveau riche - low class wannabes showing off their wealth with enthusiastic extravagance (aka bling)." Note that you can also use this term as an adjective, e.g. in a phrase like "the extravagant lifestyle of the nouveau riche."

Luxury and status symbol (from comments) are both good. There is a subtle difference between them: a luxury serves some purpose, albeit one that you could argue didn't need to be served. For example, you can go on a luxury cruise where you'll have spiffy accommodations and be waited on extravagantly, though a regular cruise would have provided most of the same benefits. The luxury status provides a boost (at some expense). If you call something a status symbol, however, you are focusing on the conspicuous consumption and not on any benefit it might provide. That doesn't mean it's useless, but that its point is to show status.

A Rolls Royce parked in front of your house is a status symbol. If you actually drive it it might also be a luxury. So, context matters.

Is folly appropriate here, or does it only apply to the spare tower you build on your castle, just to impress the neighbours? (i.e. old usage for wealthy estate owners)

I'm surprised no one offered gaud. Essentially synonymous with bling, denoting showiness and vulgarity without an implication of cheapness. It would edge out out bling in any context that antedated the late 1980s, or in contexts where the pop culture freight attendant upon bling is unwanted.

This word does not apply here but may be useful sometimes: mathom. It is in the Urban Dictionary and implies an item of too much value to discard or donate, but suitable to re-gift.

Conspicuous consumption described by Thorstein Veblen