Now to some, the very idea of taking craft away with them while on holiday sounds ludicrous. Luckily we don't socialise with those sorts of people.
The nature of the crafting materials that you may want to take away with you will vary depending on the sorts of crafts that you do. Knitting and crochet for example is very easy to do on the move. You may however get some funny looks if you try to take your pottery wheel away with you. Take kit that is practical for the sort of travelling that you do.
Try to take as little excess material away with you as you can. If you want to sew some felt plushies, cut out the individual pieces before you go. if knitting is your thing, try to work out how much yarn you will need before you go.
Different airlines and different countries have different rules on what you can and cant take in your hand luggage. I always take a small pair of blunt nosed sewing scissors with me and I have never had a problem. Similarly crochet hooks are usually allowed (some airlines stipulate they must be made of plastic). If in doubt, check with your airline first.