If you want to spend hours or days handcrafting and tuning, there are plenty of options, but for quickly making diagrams that still look good (and can be fine-tuned to look even better) I find Visio hard to beat. It's Windows only and costs money, but it is well worth the money.
Thanks for mentioning Visio, it is now available on the browser as well for basic, business, flowcharts, network, and cross-functional flowcharts. $5/per user/per month (annual plan)
https://products.office.com/en-us/visio/visio-online-plan-1
Disclosure: I work for the Visio team, so if you have any feedback pls lmk.
What drives me absolute bananas is the way they changed licensing for Visio. You could get the database reverse-engineering feature (Pro version) for a fixed, one-off price up to some point. Now it's all subscriptions. Blah.
(great software though, I have to admit)
As for the main topic, my favourite diagramming tool is GraphViz, mostly because it is easy to script / automate, does a great job auto-placing things, handles large diagrams quite nicely and works on any OS.
