terminology - What do all those cryptic number and letter codes in a lens name mean?

When looking at a lens name, there are a lot acronyms describing its features (often specific to the manufacturer).

Examples, Nikon:
Nikon AF-S DX 16-85mm VR f/3.5-5.6G IF-ED
Nikon AF-I 600mm f/4D IF-ED
Nikon AF-S VR Micro-NIKKOR 105mm f/2.8G IF-ED

Examples, Canon:
Canon EF 85mm f1.2L USM Mark II
Canon 70-300mm f/4.5-f/5.6 DO IS

Examples, Sigma:

Sigma 150mm F2.8 EX APO DG HSM Macro
Sigma 70-200mm F2.8 EX DG OS HSM
Sigma 50-150mm F2.8 EX DC APO HSM II

How do I decipher these lens codes from different manufacturers?

Answer

^{Note: Because of the community-wiki nature of this question, this accepted answer became really long, and difficult to edit and keep current as lens designations evolved. The historical answer has been broken up into individual answers per lens brand, with links to each of the lens brand answers below.}

Descriptions by Lens Make

Brand Lenses

All major camera manufacturers offer their own line of lenses. Such lenses tend to follow the most stringent quality guidelines, and often come with a price premium.

Off-Brand Lenses

Most off-brand lens manufacturers make lenses that fit many types of bodies, including Canon, Nikon, etc.

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Descriptions by Lens Features

If you know what feature you're looking for in a lens (cropped-frame designation ultrasonic motor, low-dispersion elements, image stabilization, etc.), and want to know what each of the brands call that feature, the following answers are organized by lens feature.