Motorcycles

Before you get involved with spare tubes, spoons, trail jacks, etc. Stop, drop, and roll: Get a bottle of Slime, and apply it to your tubes per the instructions as a preventative measure. In my experience, the majority of trailside punctures and flats can be prevented entirely with Slime (or a similar product). The best way to change a tube in the middle of the woods is not to have to.

Otherwise, tube changes will require more than just a spare tube and some spoons, and I find that usually people aren't thinking about that until it's too late...

For tube brands, anything with a brand name you recognize is probably good enough. Avoid crazy non-brand vendors. I've had decent luck with Tusk tubes, Goodyear, Double Tough (usually sold locally at Cycle Gear stores, also), Michelin, and Kenda. You can get regular thickness or the "heavy duty" type; I've never found much benefit in the ultra thick mega heavy monster duty 3, 4, 5, or 6mm tubes and these take up progressively more and more space in your kit the thicker they are. They don't actually stop punctures any better (anything that's strong and pointy enough to make it through your tire carcass will laugh at any tube of any thickness) but they cost more, weigh more, are harder to work with, and take up more room.

You also need a way to get air into the tire afterwards, like a portable pump you can connect your bike's battery. You also need a way to get the wheel in the air, especially if you have a heavy ADV bike you don't feel like lying on its side to get the axle and wheel out, and a way to bust the axle nut loose which will probably be hard to do without packing some kind of cheater bar to put on your wrench. I use the BikeMaster Lift Stick as a trail jack for my KLR, and it lives in my panniers along with my tire change stuff all the time. It's also handy for assisting with chain cleaning and lubrication on long trips, etc. Employed carefully, it can lift either the front or rear wheel.

I prefer aluminum tire spoons because they don't beat up your rim as much as steel ones, and they are not prone to being cheaply chrome plated like many steel ones also, the trouble with that being that the chrome plating flakes off and turns itself into little razor blade shards almost immediately which will obviously cause you grief. It's much easier if you develop a burr on your aluminum spoons to smooth it out on a Rock Or Something also, vs. a steel one. I have this Stockton set which doubles as a pair of axle nut wrenches. Different size kits are available, so get the one that matches the axle/nut sizes on your bike.

HD tubes are bulky and heavy so what I did was I took the stock tubes out to keep as spares and put the HD tubes in so that I'm less likely to even need the spares anyway. The HD tubes just take up too much space for me to keep the on hand as spares.

In addition to spare tubes, you also need a way to remove the wheel from the bike so make sure you have tools for that. For tire irons I use the Motion Pro levers or maybe the Tusk knockoffs, I can't remember which but they're basically the same. You'll also need an air compressor to reinflate the tires. It's also helpful to have a valve stem puller in order to fish the valve stem through the rim because sometimes it's a pain.

I'd also recommend practicing at home, maybe when you swap the stock tubes for HD tubes so that you know what you're up against. Everything is more difficult on the side of the trail.

Personally I don't ride my tubed bike very far from home base so I don't bother carrying tubes or tire changing tools because it'd be easier just to have my wife come pick me up or meet me with a tube/tools if I need them.

I'm probably going to give the Tubliss system a try because having to change a tube to fix a puncture sucks. A proper tubeless wheel and tire is the best option IMHO because all you need is a rope plug kit and an inflator. Tubed tires need so much extra crap that I just don't like carrying on a day trip.