I like to travel light:
- My Rema Tip Top Touring Puncture kit (small green pastic box) also holds a £20 note, some change and 2 chain links as well as the puncture kit.
- I take one tyre lever as that's all my wheels need. If I forget this, the quick release lever will do as a substitute.
- A Blackburn Aluminium mini pump (works best if you place the valve end on a rock or kerb edge so that you only need to push it like a track pump)
- A mobile phone and enought food for the ride also goes in my pocket.

Back when I was at school, I found that most tyre-related things can be bodged if necessary, for example packing MTB tyres with grass, or patching splits with newspaper works OK. Now if the tyres are looking at all worn out I tend to replace them as it's much better to do at home than getting punctures every half hour.

If I were going on a longer ride I'd probably also take a multi tool. If I am going on a group ride I also take an inner tube to avoid keeping others waiting if I puncture.