I prefer not to check a bag simply because it speeds up the process and minimizes risk.

The longest I've gone carry on only is probably around 10 days. Most certainly can go longer but I don't usually go on trips longer than that. The exception to that is next month when I go on an 18 day trip to Australia/New Zealand and SE Asia. Going to be tricky as I need some warmer clothes for Australia/NZ but I think it'll be doable, especially with a laundry stop somewhere in between.