The short answer is yes, just remember the 3 cardinal rules

Think small (socks, mitts, hats)
Use wooden needles
Remember to remove scissors/tapestry needles (use tiny snips instead)

There is of course a much longer answer to this which is that, like so much in life, it depends.

There is a common misconception that the individual airlines set the rules, but for the most part the airlines are bound by the commercial regulations pertaining to the countries they are operating from.

In the UK this information is available on the gov.uk website, which specifically states that knitting needles are allowed in cabin baggage. The final decision though rests with the security staff on duty and they have the right to confiscate anything they deem to be a security risk. It is extremely unlikely that you would have your needles confiscated but there are a few things you can do in advance to mitigate this risk.

Stick to wooden, rather than metal needles and avoid taking your most expensive set with you. Only take needles that you wouldn’t be upset to lose.
Run a lifeline through your work prior to leaving. That way if you do have to remove the needles and hand them over you won’t lose your work.
Don’t bother taking a self-addressed envelope with you (as some advise - so that you can post them back to yourself). Think about it - due to security concerns when was the last time you saw an open post box in an airport concourse.
Make sure to remove any scissors or tapestry needles from your project bag. You can buy little Hiya Hiya snips with tiny blades, Clover do a little cutter (although I have heard of these being confiscated too). In a pinch a dental floss container - and it’s little integral blade can cut most yarns.
Please don’t try to hide needles in other baggage or on your person. I’ve heard of people hiding needles in their hair and honestly I can’t imagine an easier way to get pulled over and pat searched for suspicious activity. Be honest, up front and be prepared to demonstrate your knitting. From personal experience I have had security agents confused by circular needles, as they expect to see long, pointy ones. Circular needles may sometimes require an explanation.

So, there you have it. It’s not rocket science and with a few exceptions most countries have no issue with you flying with needles - Mexico is known for being particularly strict I hear.

Avoid hearsay and rumour

Few things are likely to elicit more of a response than posting this question in a Facebook group so please save yourself the time and bother. You’ll get a flood of contradictory advice from people in different countries and operating under a different set of assumptions. People will tell you to

Call the airline
Call your holiday operator
Yes, you can
No, you can’t
Sometimes

Honestly, it’s not worth the hassle - check the regulations for the country your flight is leaving from:

UK: Hand luggage restrictions at UK airports: Personal items - GOV.UK (www.gov.uk)

USA (TSA): Knitting Needles | Transportation Security Administration (tsa.gov)

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