Not so much apps, but utilities! Little things make a difference
For the tab-happy, it’s the hassle-free saviour of your battery: The Great Suspender.
1Password is invaluable (sync’d to my iPhone and iPad too, that way I’m never left without important info, including saved scans of passport, bank codes, PINs, etc.).
Another vote for Flux —same as Settings>Display>Night Shift on recent iOS devices.
Everyone knows how troublesome it is when the WiFi or net drops off, well CirclePing gives unobtrusive menubar feedback when the network connection is bad (has high latency). HowOnline or Autoping give more detail if you’re techie (I’ve yet to find the perfect app though).
Indeed as a techie, I like to keep a bit of an eye on the system, as there’s nothing worse than a runaway program using all your bandwidth/CPU/battery, but I’m not too fond of unnecessary menubar icons (e.g. battery when fully charged, waste of space!) so I use iStatMenus. Plus it has a really useful calendar view with multiple clocks for different zones.
Karabiner is great for customisng the keyboard (like changing the right-hand alt key to an enter key), and BetterTouchTool is just fab for setting up custom swipes and finger taps to do stuff for you per-app. (swipe to tab-indent, swap to fullscreen, change apps with a tap… possibilities are endless, if you can remember what)
iBooks once setup for iCloud, is good for syncing PDFs between devices, else ‘send to Kindle’.
Again if you have an iPad, DuetDisplay turns it into a second display, so yeah you can write full screen and keep Twitter open at the same time. (Okay, that’s not really so wise.)
Finally (okay maybe not, but certainly for now…), I use the built-in Yahoo stocks dashboard widget† to get current exchange rates with graph, so I don’t miss opportunities to do transfers at good rates. Just enter the currency codes together instead of a stock symbol, e.g. USDEUR, once added click the symbol to expand with graph. †Dashboard is not enabled by default any more though, so preferences>mission control>dashboard:as overlay then show dashboard:F4.