Every developer has their favorite set of tools. I have written about a few of them so I'll link to those tips. Here's what I use mainly for iOS app development (in alphabetical order):
AppCode is worth using just for the refactoring tools, quick-fix functionality and inspections.
A proxy server that lets you examine HTTP(S) requests made by (other) apps.
A third-party documentation viewer. Viewing documentation in Xcode used to be very slow. Dash was much faster, but the speed difference is not so significant anymore.
A very handy tool for reducing the size of your PNG files.
A pretty diff tool
I write most of my code in MacVim. Still one of the faster way to enter and edit text.
A tool that lets you make HTTP(S) API requests and display the results in a nice format. Supports extension which generate code you can copy and paste to make the same requests in your project.
I built this app so I can work out regular expressions as well as test them.
Similar to ImageOptim, but for PDFs.
An excellent vector drawing app. Has great support for generating images at different resolutions — especially useful for app icons and in-app assets — with the click of a button.