The Romans did try to expand in to Germania, and almost had the entirety of Germany in their hands.

Their first major forays in to Germania were under Julius Caesar, who found that tribes along the Eastern side of the Rhine to be causing trouble along his minted Western shore during his conquest of Gaul. In a show of support to his Eastern-shore Germanic allies the Ubians, Caesar built a large wooden bridge in just 10 days which acted as this 'look at what we can do -- this river won't protect you' move. He was only across the Rhine for a couple of weeks, and then he went back West and took the bridge down.

Later in his Gaulish campaign, he built another bridge to confront the Suebi, but encountered little resistance so he returned to Gaul. [Gallic Wars, Caesar]

Next big foray was in to Dacia by Domition, of the Flavian dynasty. Domition was eager to earn military laurels, but was pushed back by Decebalus, the king of Dacia. 20 years later, under the command of Trajan, Decebalus was defeated (101-102AD) and allowed to keep his throne as a client King of Rome, acting as a buffer state against the tribes to the East. He even shrewdly negotiated for Rome to pay him (despite losing) so he could 'build fortifications' on his East. However, he used the money to bolster his defenses in the West, against Rome. Feeling he was in a strong position, in 105 he launched attacks in to Rome -- Rome/Trajan promptly replied with a decisive invasion that deposed Decebalus and established Dacia as an imperial territory. Dacia was expensive and difficult to defend, but its rich gold mines propped up the ailing treasury and was enough of a boon to Roman finance that Hadrian did not rescind Roman control.

During the reign of Marcus Aurelius, the Marcomanni and Quadi became increasingly belligerent across the Rhine, and so an extensive and long Germanic campaign was undertaken. Rome systematically began fighting for territorial control over the confederated tribes of the East, and would most likely have taken Germania in total had not Aurelius died, leaving the throne to his biological son Commodus (incidentally, the first Emperor to ever have been born 'in to the purple', that is, born as the son of the Emperor). Commodus, 16 at the time, simply wanted to return home, so he offered the near-dead Germans a treaty despite the complaints and pleas from his generals to allow them the chance to complete the campaign. His treaty returned most of the land to the Germans and is a pretty huge turning point in the Empire -- as had he let his general continue, Rome very well would have grown considerably.

The treaty lasted, however, and there was no major campaigns or invasions for about 90 years -- the Rhine becoming the apex of the East (save for Dacia). In that time, Rome would steadily lose power and stability, and instead of ever expanding, Germania would begin to invade.

Sources: Gallic Wars by Julius Caesar, the remainder cobbled from memory through reading various books on Rome and repeated listenings of the History of Rome Podcast.

The Roman forces found themselves stretched quite thin, and found it difficult to occupy far away territory's. Not worth the investment. Hence the situation in Britannia and the construction of Hadrian's wall. In many places such as Africa or far Northern Europe they stopped expanding because of the climate they were not accustomed to and therefore found it difficult to fight or harbor a worthwhile economy.

Further reading and source: http://whc.unesco.org/en/list/430/

In terms of Germany: yes. Augustus was pushing the Roman border over the Rhine right up until the Varus catastrophe which changed the strategic situation. It was a humiliating reverse and the loss of a significant portion of the standing Roman army. It seems at that point, after the punitive expeditions to remind the Germanic tribes that Roman might still existed, the calculation was made that further expansion past the Rhine wasn't an efficient return on investment.

When there was a territory that was worth it in terms of mineral resources or rich farmland then the empire would and did take it over. Trajan conquered Dacia with its rich mineral deposits which definitely benefited the treasury

There's a really good book on this subject if you're interested: Rome and The Enemy: Imperial Strategy in the Principate.