That's a very interesting question! There are very few such cases. The most (in)famous example is probably the trials of Publius Scipio Africanus and his brother, Lucius. Publius was the hero of the Second Punic War, taking the fight to the Carthaginians and finally defeating the great Hannibal in battle - the only loss Hannibal suffered in a pitched battle. Lucius stood in the shadow of his brother but had some military success in Asia Minor (with the help of his brother). Their victories gained the Scipiones (that's the plural of 'Scipio') a lot of fame, a lot of wealth, and a lot of political enemies.

One such enemy, Cato the Elder, brought charges of bribery first against Lucius (probably in 187 B.C.) and later against Publius (in 184 B.C.). These charges were patently absurd considering the fact that bribery was common and widespread among senators. The Scipiones perhaps made the mistake of being to conspicious with their wealth and getting their (alleged) bribes from Antiochus, at this time the arch-enemy of Rome. The trial against Lucius in 187 was dismissed when Publius intervened as leader of the senate, physically destroying the accounting manuscripts of his brother while accusing the senate of being hypocritical. The trial against Publius became a battle for the 'hearts and minds' of the Roman public. Livy describes the charges against Publius:

"In order to support the charges they were bringing against him, the tribunes brought up the old story of his luxurious living in his winter quarters in Syracuse and the disturbance created by Pleminius at Locri. They then went on to accuse him of having received bribes, more on grounds of suspicion than by direct proof; they alleged that his son who was taken prisoner was restored to him without ransom; that Antiochus had in every way tried to ingratiate himself with Scipio as though peace and war with Rome were solely in his hands; that Scipio had behaved towards the consul in his province as dictator rather than subordinate; that he had gone out with no other object than to make clear to Greece and Asia and all the kings and nationalities in the East what had long been the settled conviction of Spain and Gaul and Sicily and Africa, that he alone was the head and mainstay of Roman sovereignty; that under Scipio's shadow the mistress city of the world lay sheltered and that his nod took the place of the decrees of the senate and the orders of the people. No stigma of disgrace could be fastened upon him, so they did their utmost to excite popular odium against him. As the speeches went on till night, the proceedings were adjourned."(Livy XXXVIII.51)

Here we see the conspiciousness ("luxurious living") and the cases of (alleged) bribery by Antiochus, as well as a charge that Publius had behaved as if he was the head of the Roman state - a very serious charge in a Republic where power was shared between various magistrates because they hated the idea of having a single ruler.

Publius did not respond to the charges directly. Instead he addressed the people, listing his many accomplishments and making a tour round the temples of the city before leaving the city in a self-imposed exile. The trial was adjourned because of his absence (the official reason was ill health of the defendant). Shorthly thereafter Publius died and Lucius was prosecuted again. This time, without the protection of his brother, he was imprisoned. He was pardoned after paying a fine.

This is the only criminal case which really got anywhere. There have been some prosecutions of generals who had misbehaved in the field, but even that happened very rarely. Rosenstein mentions a dozen such cases between 390 BC and 49 BC ('Imperatores Victi. Military defeat and Aristocratic Competition in the Middle and Late Republic.' p.12). Note that this is a period of nearly 350 years with 4 to 12 generals in the field per year. Having only 12 in all that time is very few indeed!

Examples of generals who were prosecuted are Quintus Pompeius Aulus, who had signed a peace with Numantia without authorisation from the senate. He was prosecuted but managed to get acquitted. A couple of years later, in the same war, consul Hostilius Mancinus disgraced Rome by allowing his army to be surrounded in an indefensible position. He signed a peace (again) and made a humiliating retreat. The senate was outraged and prosecuted him. His punishment consisted of him being extradited to Numantia - nude - but the Numantians refused to accept him. Mancinus returned to Rome but was not allowed to return to the Senate. Somehow he managed to regain the trust of senators though, as later he received another praetorship (i.e. generalship) (Appian VI.80 and T. Corey Brennan, 'Power and Process under the Republican “Constitution”' p. 52-53).

These prosecutions really were the exception to the rule, and even they weren't very effective (as you've seen). Overall, one can say that the senators were in direct competition with each other, but limited that competition to areas which were not permanently damaging to others. There's some self interest at work there: if prosecutions are very rare, there's very little chance you yourself will be prosecuted...