There are a few sub-questions to this topic which will help to narrow your specific suggestions down a bit.

The first 2 are:
1) What device are you trying to connect from? (A wired microphone, a Direct Box or instrument directly, an amplifier, an analog Mixer, a USB device (An audio interface or a mixer with a USB output)
2) What device are you trying to connect to? (A new iPhone, an older iPhone, a new iPad, an older iPad, an Apple computer or laptop, an Android phone or tablet, a PC computer or laptop)

The next question is related to the first. You'll need to know what type of output connector(s) are available on the device you're trying to connect FROM, does it output a microphone level audio signal or a line level audio signal (much louder then microphone level), and is the output monaural (one channel, or stereo (two channels)?

MICROPHONES
Almost all microphones are monaural output devices and they almost always output a microphone level signal. Most will have either Male XLR, 1/4" or 1/8" (3.5mm connectors.

INSTRUMENTS
Instruments audio outputs can either be connected directly to your phone or tablet, or through a direct box that allows for a simultaneous connection to an amp. You can also connect to your device from the 'thru' connector of your amp if it has one. Most will have 1/4" jacks for output, but some may have XLR male or 1/8" (3.5mm) jacks.,

MIXERS
Most mixers usually have a left and a right output which is usually at line level. Depending on the mixer, and the on device that you want to connect to, you may have to include an adapter to lower the line level signal to a microphone level signal so that your audio does not distort, but don't even think about that part right now. Most will have either 1/4" TS, 1/4" TRS or XLR connectors

USB DEVICES
There are many devices available that include a built in USB (digital) audio output. These include microphones, audio interfaces, audio mixers and webcams. In some cases, they make it easier to connect your device to your computer, tablet, or smart phone, but that's not always true, and USB is certainly not the only way to connect your devices. These will usually have a USB Female connector.

HINTS
If you're not sure about the output connectors, or output levels of your device, you can find the answers in your equipment manual. Don't have the manual? No problem, just do a search on line and you'll probably find it. There are images lower on this page showing most of the standard connectors.

Whatever solution you decide on, tape all non locking adapter connections together when practical. Also, tape them down to relieve strain on the adapter cables. You don't want them to slip apart as you're working.

And make sure to use short jumper cables or adapter cables when connecting to the jacks on your input or output devices. The strain of a heavy adapter on a connector can break the connector, adapter, or both.

GOING FURTHER
Input Devices: IPhones IPads And Android

Output Devices With 1/4" Output Jacks

Output Device With An XLR Connector For Output Connection

Output Devices With RCA Jacks For Output Connection

Connecting Your Mixer/audio Interface Or USB Microphone To A Tablet/Smart Phone/Computer Via USB

Connecting Your Instrument Or Keyboard To Your Device