Verified answer

To me the sonnet that expresses desire the most is sonnet 129. It is not about a particular desire for one person, but about sexual desire in general. "Mad in pursuit, and in possession so" or "in quest to have, extreme", express desire in a very clear way.

The expense of spirit in a waste of shame

Is lust in action; and till action, lust

Is perjured, murderous, bloody, full of blame,

Savage, extreme, rude, cruel, not to trust;

Enjoy'd no sooner but despised straight;

Past reason hunted; and no sooner had,

Past reason hated, as a swallowed bait,

On purpose laid to make the taker mad:

Mad in pursuit, and in possession so;

Had, having, and in quest to have, extreme;

A bliss in proof, and proved, a very woe;

Before, a joy proposed; behind, a dream.

All this the world well knows; yet none knows well

To shun the heaven that leads men to this hell.

Shakespeare mainly avoids directly expressing desire in his sonnets (the sonnets are not really much to do with 'self-expression'). But some of the Dark Lady sonnets seem to be spoken in Shakespeare's own person, and seem to suggest an actual physical passion.

Sonnet 128 is typical of these untypical sonnets. Shakespeare sits listening to the Dark Lady (or perhaps someone else) playing on the virginals, and thinks he could find better things for her to do with her hands.

How oft, when thou, my music, music play'st,

Upon that blessed wood whose motion sounds

With thy sweet fingers, when thou gently sway'st

The wiry concord that mine ear confounds,

Do I envy those jacks that nimble leap

To kiss the tender inward of thy hand,

Whilst my poor lips, which should that harvest reap,

At the wood's boldness by thee blushing stand!

To be so tickled, they would change their state

And situation with those dancing chips,

O'er whom thy fingers walk with gentle gait,

Making dead wood more blest than living lips.

Since saucy jacks so happy are in this,

Give them thy fingers, me thy lips to kiss.