In the past, I've gone through various phases of what I carry on the bike and how: I've went through fanny packs, saddle post bags, whatever, and have carried lots of useless crap in the past...
Today, my optimized scheme is good for day-long sufficiency in group and solo rides and consists of a waterproof pouch that fits in a single jersey center pocket. (If you're going to go the saddle bag route, I suggest the sugoi minibago or bigobago if you can find it for sale)
In there I fit two road tubes (I keep them in their box packaging, helps make it fit) two co2 cartridges along with a mini inflator a super thin multi-tool which includes a chain tool, a couple 10-speed missing links (make sure these match the chain you're using - brand and speeds) and a thin leatherman pliers multi-tool and also a very thin and small spoke wrench for 3 kinds of spokes. In there I also have a couple tire patches, some alcohol pads for cleaning, and a folded $20 bill for emergencies.
Outside the pouch I pack - two snap-in yellow pedro's tire levers (the best) and in a plastic sandwich bag my phone keys and money/cards/id moneyclip. If its a big group ride, I get two more tubes in the side pockets. The most bulk are the tubes and co2s, the tools I've selected the very thinnest possible ones so they fit in nicely, and everything else is paper thin. (I've tried many portable pumps (currently I have a full sized frame pump) and they are all incredibly tedious to use which is why co2 is my first choice. As far as I'm concerned, co2 will last you a day's ride, but as soon as you get home you definitely want to deflate and reinflate with air, because overnight the co2 will lose pressure. My road tires are at 120psi before every ride (you can check on the side wall what yours are rated are) and the CO2 gets it up to about 100psi.)
On the road I have encountered four basic mechanicals that are catastrophic enough to stop you from continuing to a bike shop (this is why I don't carry replacement cables, for example - if you pop a cable you can still relax the brake, or just not shift on that particular side, but still get to a bike shop hopefully)
1) The flat tire. This is what the tubes, co2, and tire levers are for (and I have a backup frame pump, I got tired of the little ones) I also use the pliers to get embedded wire snippets/metal shavings and whatnot out of the tire that caused the flat in the first place. (I always inflate before a big ride so I don't get pinch flats) (What is this gel inside the inner tube? I've never used any gel for flats, except the sealant for tubeless clincher tires, but I got tired of that shit and went back to good ole inner tubes. Oh yeah - the outer tires I have are kevlar puncture-proof, these kind of tires weigh more but they're worth it, I've had drill bits get embedded in the outer tire but not puncture the inner tube!)
2) The popped spoke. This is what the spoke wrench is for. (I really would like to find a tool that has the multi tool, chain tool, pliers, and spoke wrench all in one and is thin enough...) Basically a popped spoke de-trues your wheel enough that even if you relax the brakes all the way, it will still be rubbing enough to slow you down and possibly pop the tire by friction. (The long term solution is to lose weight and/or get a higher quality wheelset.) What you do is use the spoke wrench to relax (undo half a turn or so) the two spokes that are next to the popped spoke, and that's a poor man's truing solution until you can get to a bike shop and replace the spoke.
3) The broken chain. This is what the missing links and chain tool is for. While I've seen people repair chains without missing links, the missing links are small enough and useful enough that I prefer them instead. (Once a chain breaks on you, you need a new chain, and I suggest researching chain life and getting a new chain well before that.)
4) Everything else (severly bent wheel, cracked frame, etc) this is what the phone and money is for to call for transportation.
Of course this is probably overkill for a 20 miler, but all of this has been a life saver to me when you're out in the middle of nowhere, 4 cycling hours from home.