I use a backpack when I'm going places on foot or public transport. Pretty essential when I need to be carrying a few things with me.
When I ride my bike it depends what I am doing when I get off my bike. If I don't need much other than phone, water, keys and my wallet. I use this old Polish army satchel which whilst hideous, is just the right size for all those things and it has a waist strap so is perfect for using with my bicycle.
Backpacks aren't the most fashionable things, so I think it's totally okay to just go something that is totally utilitarian.