As others have said - it's up to the photographer. Short answer - of course you can do fine without a tripod for anything but slow shutter shots, and if handheld is your preference, go to it. Personally, I only use a tripod when I know I'll be taking shots at shutter speeds of 1/2 second or less, consistently. Sometimes that may be daytime too, like when I'm using ND filters for long exposures...but generally, it's mostly at night. And sometimes even at night or for longish exposures, I didn't feel like bringing the tripod, or didn't necessarily plan on long exposures, and will get by handheld relying on image stabilization, a good steady stance, and/or something to lean on or support with.
Having traveled extensively through the Caribbean every year for the past 30 years...I can say I've only once ever had a tripod set up on island ground - to do some night shots of a ship at dockside. I've used tripods on board ships for long exposures, but for landscape, scenic, architecture, walkaround, and HDR, I've gone handheld.
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 200-500mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony NEX5N / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / Pentax K adapter / Konica K/AR adapter / bunches o' Konica & Pentax lenses!