Yes, and yes, I always have a spare tube and a pump on every ride I go on, I also take patches on every ride I go on, as well as the obvious a set of tire irons which I happen to prefer the Soma Steel Core Levers. On my touring bike however due to tires with extremely tough sidewalls and their wired beaded I also carry a VAR tire lever, this makes snapping on the last couple of inches a lot easier then using tire levers, I just use the tire lever to put on the easy part and to make sure the tube is out of the way before I use the VAR, the Var is also small enough to fit into my seat bag.
On the subject of flats I'm backwards from most of the crowd, I always will try to fix the flat with a patch first before going to the tube, why you scream? Because 7 times of 10 I can find the offending object in the tire, I make a mental note of where that object is by finding a tire marking (this is why it's important to index the tire to the tube, meaning the valve stem should be located on a particular letter, usually a middle letter, on the tire so you know where the tube was on the tire after you removed the tube so you can place the tube over the tire and know where the hole is generally), I most of the time LEAVE the wheel on the bike(!) if it's a foldable bead tire type, then I remove about half of the bead on one side of the tire with the offending hole in the center of the half, then pull out about a 1/4th of the tube again with the hole being in the center of the fourth, look for the hole which is usually visible if you stretch the tube with your hands to make the area larger, buff the area, wipe with a alcohol patch and apply a glueless patch. Yes a glueless patch made by Park if done correctly will hold on the tube forever with or without air, I press the patch on for a hard as I can between my thumbs and fingers for 30 seconds look at the patch for any frosty areas and repress those, reinstall and go. Doing it this way is faster then putting a new tube in, rolling the old one while removing all the air to make to compact enough to put in a saddle back then later have to go home and waste more time trying to find the hole and patch the tube.
Of course if I can't find the object I may have to remove the tire and tube, put some air into the tube to get the tube about 2 to 3 times it's normal size and then pass the tube across my ear till I feel and or hear the leak, patch as above, lay the tube on the tire as I had previously indexed it, and try to find the offending object stuck in the inside of tire, I use my bare fingers, some say ouch but i clot fast if by chance I poke myself, so it will stop bleeding in less then a minute, those of you don't like that take a cheap small cotton rag and rub it along the tire till it snags on something.
If by some slim chance I can't find the leak I go to the spare tube and wait till i get home to do the water in a basin leak finding test.
I heard one guy say he rides very light on his rides, that's fine, but if I have a breakdown I'm going to and want to be prepared for most things. So yes, I carry all the things I mentioned in my first paragraph plus a Park MTB 3.2 mini tool, and a pair of cheap small folding pliers, plus other small odds and ends to make sure my trip continues so I don't have to either turn around and head home cutting my journey short, or calling the wife which I've only had to do twice in 40 years of being married to her while cycling.
Speaking of pumps and cutting your trip short, the vast majority of mini pumps on the market today are only designed to put 70 or so pounds of air in a tire so you can get home no matter how high of a pressure they claim they can go, to that I say BS! If the pump can't get my tires to 100 psi without being a gorilla to do it it's not a pump I'm going to buy. There are only a few pumps that will get you to 100 that I know of, one is the Lezyne Road Drive large size (the two smaller sizes I doubt seriously, especially the smallest one, will get you to 100); Lezyne Carbon Drive Lite; the next one is Topeak RaceRocket HP, this one will take more strokes and effort then the Lezyne but will get you there; Birzman Velocity with the gauge; Blackburn Airstik SL; and this last one is the easiest but it's also the largest, heaviest and ungainly looking pump, plus the mounting system sucks, but it's the Topeak Road Morph G, this is like have a mini floor pump on the road. I prefer the pumps with hoses these days because tube manufacturers in the interest of saving a penny on each tube have take away the reinforcement washer that secured the stem to the tube thus a lot of people have a tendency to "saw" the pump back and forth (especially as the PSI goes up) which in turn could rip the stem from the tube forcing you go to your backup tube or patching the one you thought you were going to fix when you got home.
Also in regards to pumps I didn't mention CO2 because I don't like them, it requires that I buy air that I can get for free, it requires that I take the empty canister home and dispose of it properly (some cycling jerks throw theirs on the side of road which is where I see them all the time), never know if by chance you might need more air then you carried (of course carrying a backup pump will resolve that issue but that defeats the purpose of trying to travel a bit lighter), then because I hate doing things twice it requires that you go home and drain all the CO2 air out of the tube because CO2 air can lose about 50% of it's pressure in just 24 hours, and if you don't get all the CO2 air out any remaining CO2 after a top off will leak out almost as fast as it did the first time, so your back to filling more often; anyway all around it's extra money and work I don't want to hassle with, if I was racing I would use CO2 otherwise forget about it. For those who still want to use CO2 you can get hybrid pumps that off the best of both worlds in a smaller all in one package then going with separate inflator and a pump but still more weight than just a pump by itself.
Sorry it's Saturday and I went off too long.