Other movements

поднимать/поднять рукуa (or рукиa) to raise one's arm(s)/hand(s)
Поднимите руки вверх и согните в локтях. Raise your arms and bend them at the elbows.
NB The above expression is also used in reference to voting procedure:
Кто за это предложение, прошу поднять руку. Whoever is for the proposal, raise your hand.
Руки вверх! Hands up!
NB The above phrase is an order to surrender.
опускать/опустить рукуa (or рукиa) to lower one's arm(s)
стоять [no Pf.] рукиn по швамd;
стоять [no Pf.] рукиn навытяжку
to stand at attention (lit. "with one's arms at one's sides")
NB The phrases стоять руки по швам and стоять руки навытяжку, above, describe a response to the military command Смирно! "Attention!"
прикладывать/приложить рукуa к козырькуd to salute
NB The gesture described above is used in the military.
висеть/повиснуть: у Ng бессильно висят рукиn; у Ng рукиn висят, как плети N's arms hang listlessly
сгибать/согнуть рукуa (or рукиa) to bend one's arm(s)
разгибать/разогнуть рукуa (or рукиa) to straighten one's arm(s)
разводить/развести рукиa (в стороныa) to spread one's arms
разметать [no Impf.] рукиa в стороныa;
разметать [no Impf.] рукиa во снеp
to fling one's arms out (in one's sleep)
Мальчик спал, разметав руки в стороны. The boy was asleep, his arms flung out to the sides.
отводить/отвести рукиa назад to put one's arms behind one's back
NB The above phrase describes the motion of putting one's arms behind one's back, then arching them upwards; it is a gesture made by someone about to dive, or while doing calisthenics.
вытягивать/вытянуть рукиa to stretch one's arms out
висеть/повиснуть на вытянутых рукахp to hang by the arms
подавать/подать рукуa Nd to offer one's hand to N (in order to shake hands)
Вот тебе моя рука! You have my word on it. (lit. "Here's my hand!")
NB The above phrase accompanies an extended hand, and is usually used when one is making a promise, offering help, or extending friendship.
протягивать/протянуть рукуa Nd to extend one's hand to N
NB The above phrase is used to describe an offer to shake one's hand.
(крепко) пожимать/пожать рукуa to shake someone's hand (firmly)
Я протянул ему руку и он крепко пожал её. I held out my hand to him and he shook it firmly.
стискивать/стиснуть Nd рукуa to squeeze N's hand (in a firm handshake)
припадать/припасть к рукеd to kiss someone's hand
Я припал к её руке. I kissed her hand.
приставлять/приставить рукуa (or рукиa) ко ртуd to cup one's hand(s) around one's mouth
NB The above phrase describes cupping one's hand(s) around one's mouth in order to magnify one's voice.
смотреть [no Pf.] из-под рукиg to shade one's eyes with one's hand
NB The above phrase is used to describe a gesture used to protect one's eyes from the sun or other sources of light.
совать/сунуть рукуa в карманa to put one's hand in one's pocket
сжимать/сжать рукуa (в кулакa) to clench one's hand (into a fist)
разжимать/разжать рукуa (or кулакa) to unclench one's hand/fist
протягивать/протянуть рукуa (or рукиa) к Nd to extend one's arm(s) toward N
Он протянул руки к огню (or к Наташе, etc.). He extended his arms toward the fire (or to Natasha, etc.).
подносить/поднести рукуa к Nd to bring one's hand close to N
отдёргивать/отдёрнуть рукуa от Ng to jerk one's hand away from N
NB In the above two expressions N cannot refer to a person.
скрещивать/скрестить рукиa на грудиp to cross one's arms over one's chest
закладывать/заложить рукиa за спинуa (or за спинуa) to put one's hands behind one's back
Он нервно бегал по комнате, заложив руки за спину. He ran around the room nervously with his hands behind his back.
заводить/завести рукиa за головуa (or за головуa) to raise one's arms and place one's hands behind one's head
NB The above phrase describes a motion made by someone stretching or doing calisthenics.
закидывать/закинуть рукиa за головуa (or за головуa) to clasp one's hands behind one's head
NB The above phrase describes a position of relaxation, whether one is sitting, lying, or standing.
обнимать/обнять колениa рукамиi to hug one's knees
махать/помахать, махнуть [Pf-once] Nd рукойi to wave to N
NB The phrase махать N рукой, above, usually describes a gesture of farewell, as distinct from the phrase махнуть [no Impf.] рукой на N meaning "to give up, to decide not to worry or not to bother about N."
Брат махнул нам рукой и скрылся за поворотом. My brother waved to us, and then disappeared around the curve.
размахивать [no Pf.] рукамиi to gesticulate too much; to wave one's arms
NB The above phrase indicates broad gestures, such as waving one's arms to call attention to oneself, swinging one's arms as one walks, or gesticulating excitedly in conversation.
Не нравится мне этот актёр: кричит, размахивает руками. I don't like that actor; he screams and gesticulates too much.
взмахивать/взмахнуть [Pf-once] рукамиi to wave one's arms, to flap one's arms
Он как-то странно взмахнул руками и упал. He flapped his arms in a strange way and fell.
обвивать/обвить рукиa вокруг шеиg Ng Bookish to twine one's arms around N's neck
NB The above phrase describes a gesture most often made by women and children.
Она бросилась к мужу и обвила руки вокруг его шеи. She ran to her husband and twined her arms around his neck.
обнимать/обнять Na to hug, embrace N
ходить [no Pf.] (or гулять [no Pf.]) под рукуa to walk/stroll arm-in-arm
брать/взять Na под рукуa to take N's arm
брать/взять Na под рукиa to grasp N under the arms (to support or restrain him)
Санитары взяли больного под руки. The orderlies supported the patient under his arms.
держать [no Pf.] Na под рукуa to have N on one's arm
Молодой человек держал под руку девушку невысокого роста. The young man had a petite young woman on his arm.
NB Note that only the singular form под руку is used in this sense in the above expression; for an expression with the plural form, see below.
держать [no Pf.] Na под рукиa to hold N under the arms (to support or restrain him)
Солдаты крепко держали арестованного под руки. The soldiers held the prisoner tightly by the arms.
отводить/отвести в сторонуa рукуa to push someone's hand away
Шофёр отводит в сторону руку Олега с рублём. The driver pushed Oleg's hand with a ruble in it aside.
выводить/вывести Na за рукуa to take N out by the hand
NB The above phrase describes a punishment, usually of children who have misbehaved.
Колю вывели за руку из-за стола и отправили спать. Kolya was taken by the hand from the table and sent to bed.
предлагать/предложить Nd рукуa to offer N one's arm
опираться/опереться на рукуa Ng to lean on N's arm