The Rode VideoMic Me (appx. $57) has a flexible mounting bracket that can accommodate a variety of phone models and uses power supplied by the connected device. It is best suited to dialogues and interviews, though, rather than picking up ambient sounds.
The Apogee MiC 96k Professional (about $229) can connect to any Apple device through its Lightning port to become a high-quality studio tracking microphone. Note that it's better suited for doing voice work in a tuned room than it is for field work.
About as simple as they get, the Movo MA2010 (about $14) sports an omnidirectional pickup pattern and has an audio output passthrough, so you can monitor exactly what you're laying down. It works with nearly all devices and is backed by a 1-year warranty.
For owners of modern smartphones, like the newest iPhones and Samsung Galaxies, the Shure MV88+ (appx. $249) can automatically adjust its equalization, compression, and limiting based on the sound environment it detects, keeping your audio clean and clear with little to no clipping.
They don't get much smaller or less expensive than the Saramonic Mini SmartMic (appx. $25), which has a directional condenser configuration that makes it useful in a wide range of situations. It weighs under an ounce and is compatible with almost anything that accepts a 4-pole plug.
The Shure MV5 (around $99) features flat-, vocal-, and instrument-focused DSP presets, making it easy for beginners to use and still get a high-quality recording. An integrated headphones port allows for real-time monitoring, and it's MFi-certified for use with Apple products.
The Saramonic SmartMixer (about $150) is a two-channel kit that turns any smartphone into a professional rig. It features a pair of inputs, LCD level monitoring, phantom power, and an amplifier for studio-quality recording anywhere you happen to be.
In addition to a typical 3.5-millimeter model, the Comica CVM-VS08 (about $45) comes in a USB Type-C version that's compatible with many of the newest devices. It's also available in an ultra-compact form factor that's especially easy to carry around and sounds almost as good.
Quality engineering and a low price combine to make the Movo PR-2-PM (about $54) one of the most cost-effective models around. It comes with a shock-resistant mount and a deadcat windscreen to help ensure your mobile videos sound as good as they look.
With all the expertise that the company gained designing some of the film industry's finest shotgun microphones, the Rode SmartLav+ (about $65) provides near-movie-quality sound from a device that's especially easy to hide on a performer's body.