Old-fashioned is a tricky word for lexicographers. It has only one meaning, but several possible interpretations (or ‘readings’, as linguists often call them). This is reflected in the Macmillan Dictionary’s entry, which starts with a neutral definition (‘no longer modern or fashionable’) but goes on to indicate that old-fashioned can have both positive and negative readings. Things can be out of date and no longer fit for purpose, as in these corpus examples:
Paula had no patience for making conversation with Gran, who tended to have very old-fashioned, dyed-in-the-wool ideas.
Over the last twenty years [the Civil Service] has seemed old-fashioned in aspects of its training, culture, and approach to policy-making.
Alternatively, old-fashioned can encode feelings of nostalgia and affection, especially for forms of behaviour which (to the speaker’s regret) are dying out. This use – frequent collocates include courtesy, charm, good manners, and romance – is also popular as a marketing ploy in tourist guides:
The tiny harbour town of Alexandria is home to old-fashioned ice-cream parlours, antique stores and home-style restaurants.
Ideal for a special break, here you will find good old-fashioned hospitality, delicious food and a relaxing atmosphere.
This is a good example of what the lexical semanticist Alan Cruse calls ‘contextual modulation’*. The basic meaning doesn’t change, but the context highlights one particular aspect of it – in this case, the speaker’s attitude towards the thing being described as old-fashioned. This in turn reflects our ambivalent feelings towards the idea that change is always good and ‘progress’ always means improvement. Consequently, it’s not unusual to find people describing themselves as old-fashioned:
I am old-fashioned enough to want to cling to the ideal of a close-knit family.
I suppose I’m rather an old-fashioned teacher in that I give quite a lot of tests.
These admissions are often prefaced by maybe or perhaps, and followed by but:
Maybe I’m just being old-fashioned, but back in my day … you didn’t buy a house you couldn’t afford.
The effect is to concede that old-fashionedness is generally seen as a bad thing, while asserting that you think your old-fashioned views happen to be right.
The word Luddite means old-fashioned too, but in a more specific way: Luddites dislike and distrust new technology. The original Luddites were textile workers who opposed the introduction of new machinery during Britain’s industrial revolution. Essentially it was an argument about ‘deskilling’ – what happens when machines take over what used to be a skilled job, and can be operated by low-skilled (and therefore low-paid) workers. The 19th century Luddites didn’t just engage in peaceful protest: they smashed the hated new machinery. The government responded ruthlessly by staging mass trials, and jailing or even executing those found guilty. The trials took place 200 years ago this month, in January 1813, and a website marking this anniversary has been set up ‘to honour the Luddites’ struggle and challenge the myths about them’. It rejects the charge that the Luddites were unthinking enemies of all new invention, and it stresses the relevance of their 200-year-old cause to debates going on now about technology, progress and the workplace.
While words like dinosaur or fuddy-duddy are unambiguously critical of people who are felt to be out of touch with modern realities, Luddite – like old-fashioned – is capable of a positive ‘reading’ too, and is sometimes used by people to describe their own, not very enthusiastic attitudes towards the latest electronic products. But its most frequent use seems to be in formulas like ‘I’m no Luddite, but…’ , where speakers defend themselves against the implied charge of being anti-technology. It seems that most people don’t like being characterized in this way, but they are also anxious not to be seen as uncritical slaves to every new high-tech gizmo. This fits with the efforts of the ‘Luddites at 200’ website to ‘rehabilitate‘ the word. For them, being a Luddite does not mean ‘denying the real benefits of some technologies’, but it does mean being sceptical ‘about the dogma of technology as progress’.
It would be interesting to know what words (and what metaphors) are used in other cultures to describe people who are seen as old-fashioned or opposed to innovation.
Reference
Cruse, Alan. Meaning in Language: An Introduction to Semantics and Pragmatics. OUP 2004.

And what about the connotations of “He gave her an old-fashioned look”? – Itself a very dated expression, I know. The Oxford Dictionaries site says says : (of a facial expression) disapproving: Jonas gave her an old-fashioned look
Thanks Claudia. We do have that phrase in the dictionary. It’s one of those funny cases where the headword is ‘old-fashioned’ and there is also a label (indicating that this usage is dated and not often seen now )- and this label also says ‘old-fashioned’ . Potentially confusing in this case, but that’s the label we use for words or phrases that are dying out but may still be encountered (e.g. in older novels).