This 32 BC denarius of Mark Anthony shows the standard of the 3rd legion on the reverse.
The 3rd were his men, and fought with him against Octavian until his defeat at Actium (31 BC). These coins were almost certainly minted to pay them.
This sculptural group in the Prado [inv. E225 - Spanish; English] is a post Renaissance composite, but the upper element is Augustan and was found in the grounds of a villa that had belonged to Marcus Valerius Messalla Corvinus. Corvinus had fought against Augustus, then joined him. The eagle represents the standard of the army, and it sits on top a pile of captured amour and shields, elements which in turn were used to make-up trophies. It looks heavily re-cut to me, and was probably 'touched up' by the sculptor who made the group.
Standards physically embodied the legion - a great coup for Augustus, for example, was when he was able to bring back to Rome the standards Crassus had at Carrhae during his ill-fated attempt to invade Iraq (53 BC). They were returned under a 20 BC peace treaty with the Parthians, along with the standard Mark Antony lost (36 BC), and others lost by L. Decidius Saxa (in Syria, 40 BC). Augustus was voted a triumphal chariot for this coup, and the standards were dedicated in the temple of Mars Ultor that he built.
Unfortunately Augustus also lost three standards as a result of Varus' disastrous defeat at the Battle of the Teutoburg Forest (AD 9).
Two were recovered by Germanicus in AD 16 - an event commemorated in this coin issued by his son Caligula when he became emperor [from Livius]; Caligula was given the nickname 'little boot' by Germanicus' men, and spent part of his childhood on the frontier.
The third standard was retrieved by Publius Gabinius in AD 41 [Cassius Dio 60.8.4]:
This same year, however, Sulpicius Galba overcame the Chatti, and Publius Gabinius conquered the Cauchi and as a crowning achievement recovered a military eagle, the only one that still remained in the hands of the enemy from Varus' disaster. Thanks to the exploits of these two men Claudius now received the well-merited title of imperator.
The last great Republican general, Gaius Julius Caesar, wrote a lengthy commentary about his campaign in Gaul. To see how important the standard was to him, do a quick word search though this English translation of De Bello Gallico.
Peter Guest believes that he has found "a legionnaire's ceremonial standard" at Caerleon: Rare artefact found at Roman site - BBC.
UPDATE - it's now a lance, not a standard.