I always carry a tool kit - for ages I tought it was silly carrying a chain splitter with me but did eventually get to use it on a friends bike whose chain snapped on a MTB ride.
My top tip is to learn how to use it - ended up taking a couple of attempts to get the thing back together so his chain ended up a bit short - at least his gears worked much better with a shorter chain!
But don't think just cause you are carrying a spare tube you won't have to walk home.... I once went for a leisurely afternoon cycle on my MTB -
1st puncture - changed the tube in the back,
2nd puncture - mended hole in back,
3rd puncture - mended hole in front, broke pump and begged help from passing motorist who luckily had a pump,
4th puncture - walked to nearby National trust property, begged my way in as had no money, sat on floor in toilets mending 'spare' tube to much tutting from old ladies. Returned to bike to discover both tires flat.
Decided to give up and phone everyone I knew for a lift home - nobody in! Walked 3 miles to nearest station - no trains on a Sunday!
Eventually walked about 8 miles home, very fed up.
Since then I often carry two spare tubes!