Major Mod Packs
There are a few “major” mod packs which are popular. These can often be used as a “base” modpack, which you can then add more mods to if you like, though keep in mind that not all mods are compatible, and you may get unexpected results when using some mods in combination with these.
Borderlands 2 Unofficial Community Patch (BL2 UCP)
The current version of BL2 UCP is 4.1, and was released in July, 2018.
Vanilla Enhanced (for Borderlands 2)
(Blame Koby for the “logo”)
Vanilla Enhanced is a pared-down version of UCP which only contains bugfixes, reskins, and some QoL changes, but without trying to affect actual balance or gameplay. For someone who is mostly interested in the bugfix aspects of UCP, but doesn’t want any gameplay changes, this may be for you. Vanilla Enhanced is available on Nexus.
Borderlands: The Pre-Sequel Unofficial Community Patch (TPS UCP)
The current version of TPS UCP is 2.2, and was released in August, 2018.
If you want to experience Borderlands 2 in a new way, this modpack is exactly for you. Currently including 155+ mods and over 650 changes! Note that BL2 Reborn already includes UCP - you should not try to use both UCP and Reborn at the same time. Reborn changes quite a bit about the game, so definitely be careful when using other mods alongside it. BL2 Reborn is available on Nexus.
For information about how to use these mods, see Running Mods.