How do I jailbreak an iPhone or iPad?
App-based jailbreaks: You will have to sideload the .ipa with Cydia Impactor or download it from ignition.fun(visit this website on your iOS device and go into the jailbreaks section). You will then need to "trust" the profile, then open up the app on your iOS device and click jailbreak.

Web-based jailbreaks: You open up the website on your iOS device and click jailbreak.

Computer-based jailbreaks: You download the jailbreak app to your computer. Connect your iOS device and click jailbreak on your computer(make sure your device is trusted via iTunes first).

No substrate/substitute jailbreaks: These jailbreaks do not support tweaks or Cydia and only give you root access. You may be able to use apps like Filza or NewTerm 2. There are currently no jailbreaks like this.

If any of the links are broken try using the Wayback Machine.

All iOS versions are currently jailbreakable

If your device is not supported, see my answer below about checkra1n, which can jailbreak all iOS versions.

11.0 - 13.5

unc0ver (app-based)

12.0 - 12.4

Chimera (app-based) (installs Sileo, a more modern alternative to Cydia)

11.0 - 11.4.1

Electra (app-based)

Important: If your device crashes/freezes frequently while using Electra, install Apple Maps.

10.0 - 10.3.3 (recommended, 64-bit only)

Totally-not.spyware.lol (web-based) (if you are wondering, it is safe, the spyware thing is just a joke)

Important: It will ask you if you want to install doubleH3lix or Meridian if your device supports both. Choose doubleH3lix unless your device doesn't have a headphone jack.

10.0 - 10.3.3 (64 bit only, only devices w/ headphone jack)

doubleH3lix (app-based)

10.0 - 10.3.3 (all 64 bit devices, use doubleH3lix instead if you can)

Meridian (app-based)

10.0 - 10.3.3 (32 bit only)

h3lix (app-based)

9.3.5 (32 bit only)

Phoenix (app-based)

9.3 - 9.3.3 (64 bit only) (recommended)

jbme.qwertyoruiop.com (web-based)

9.2 - 9.3.3 (64 bit only)

Pangu IPA (app-based)

9.0 - 9.0.2 (32 bit) 9.0 - 9.1 (64 bit only)

Pangu9 (computer-based)

9.0 - 9.3.4 (32 bit only) (recommended)

jailbreak.me (web-based)

9.0 - 9.3.4 (32 bit only)

Home Depot (app-based)

8.4.1 (32 bit only)

EtasonJB (app-based)

8.0 - 8.4

TaiG 8.0-8.1.2 or TaiG 8.1.3-8.4 (computer-based)