I have a few different modes of dealing with flats on my bicycles. They vary depending on the distance, intensity, and style of the ride I'm on; the seasons and temperature; and my mood that day. Your strategies may also differ, as I end up repairing other folks' flats far more often than my own.
TAXI or CTA
One should always have a few dollars when riding far from home, if not to take a taxi home, then at least to hop on the bus in the event of an injury or serious mechanical. In the deepest, darkest days of winter, for example -- I don't even bother with a repair kit, because a taxi is only a cell phone call away. Advantages: lightweight, simple. Disadvantages: expensive, lazy. Requires: mobile phone, cash.
CO2 Only
One of my bikes is too pretty for extraneous accessories, and so I really can't carry a pump when riding it. The CO2-only has never failed me, and I have gone through my fair share of cartridges. I use the Airchuck SL ($20), which is the smallest, lightest, and simplest inflation device on the market. It's perfect. Disadvantages: expensive. Advantages: super fast, light. Requires: Tube, tire levers, bag, cartridges, Airchuck SL.
CO2 and Pump
This is my standard mode because it's the most versatile and practical. I generally take my handlebar bag on group rides, which can easily store my tools, CO2, and a pump -- as well as clothes, cafe lock, a snack, and my camera. Unless we're in a hurry, I'll use the pump... but if I'm off the back and don't want to ask the group to wait, I'll use CO2 and easily rejoin the crew in 60-90 seconds. So if I'm carrying the handlebar bag, in goes the Planet Bike Mini Versair ($25). On my roadie, it's the Planet Bike Roadie ($30), which is far easier to use -- but not quite pretty enough for every bike. Disadvantage: weight. Advantages: versatile. Requires: Tube, tire levers, bag, cartridges, Airchuck SL, Versair or Roadie pump.
Save your patch kits for long distance touring and repairing flats at home after your ride. Your buddies with thank you for it, and you'll avoid the blown patch annoyance on the road. I recommend using either a water bottle cage-mounted toolkit (inexpensive, low center of gravity, easy to switch from bike to bike) or a medium sized saddle bag for roadies. However, once you've used a nice handlebar-mounted bag, it's difficult to go back. Mine is like Felix the Cat's Magic Bag... it seems to store endless goodies that always come in handy at the most opportune moment.