Dinosaurs seemingly had some kind of social structures: some lived in herds and provided cares to their young. Lots of anatomical features (horns, crests, claws...) were probably developed by males to fight their rivals. But estimating dinosaurs' 'intelligence' is quite difficult, since the behaviour could vary much between different species.
Table:
At least some dinosaurs (some sauropods, ceratopians, or hadrosaurs for instance) lived in herds, since tracks have been found showing lots of individuals of the same species going into the same direction. These may represent animals going to the same place at different times, for example to drink, but there are a few cases when lots of dinosaurs of the same species are fossilised at the same place, seemingly killed by a catastrophe (31 Iguanodon skeletons were found together in Bernissart).
Furthermore, the disposition of the animals in the herd seem not to have been at random: in several cases, the tracks in the middle of the herd are smaller, indicating that the young or females were protected by the strongest members of the group.
It is not clear whether or not flesh-eating dinosaurs hunted in packs. Several theropods are sometimes found around the same animal, but they could have gathered around the corpse, after the death. 
Lots of anatomical features, either weapons against predators or seemingly useless excrescences, may be linked to some kind of social behaviour. There were apparently extravagant external signs of a possible social hierarchy, maybeing at the same time sexually attracting features. These may also be used for individual recognition.
There also were weapons used in intraspecific fights against sexual rivals (several ceratopian specimens were found with puncture wounds on faces, frills and bodies).
These structures may have been brightly coloured, as in modern birds and reptiles.
This is confirmed by the fact that in lots of species, two forms are known, one of them showing less developed anatomical features, probably being a female: the ceratopian horns, the hadrosaur crests, the heterodontosaur tusks...
Here is a small list of these features. Some are clearly designed to fight against predators or to hunt, but could also deserve a social behaviour.
-
The stegosaur plates.
-
The ceratopian horns, including those whose position prevents them from being used directly against enemies.
-
The spines of spinosaurs, ouranosaurs, and some sauropods.
-
The oviraptor crests.
-
The ceratosaur and dilophosaur horns.
-
The hadrosaur crests.
-
The heterodontosaur tusks.
-
The pachycephalosaur skulls (though some think if two pachycephalosaurs were to fight one another for a female, the heads would have slipped one on the other).
-
The deinonychosaur sickle-claws (cf. the spur of cocks).
Furthermore, the crests of some hadrosaurs were hollow and connected to the nostrils. They would have been used as resonating tubes to produce varied sounds, either for individual recognition or for intraspecific communication. The same may be true for the high nasal openings of sauropods, which could hint for a trunk or for a bulb of skin.
Lots of dinosaur eggs are known. They were often laid in straight line, or in roughly circular nests. Dinosaurs probably sat on their eggs, as some adult skeletons have been found with their nests.
Some but not all dinosaurs took care of their young. A nest was found from the hadrosaur Maiasaura (hence its name) with young of varied ages, showing they did not leave the nest before several years. The youngest of them show worn teeth but very weak limbs, indicating that they were nourished from their parents.
On the other hand, the young hypsilophodonts show well-developed limbs and could probably feed themselves early and run away from predators.
Troodon nests have been found and contain about twenty big eggs, grouped in pairs. This means that Troodon had a dual oviduct system (like Sinosauropteryx, but contrary to most birds), and that two couples of eggs were separated in time. Small litters and big eggs, as in birds, are a strong hint in favour of cares to the young.
An Oviraptor has been found brooding on a nest of some twenty eggs. No remains of a heap of plants were found on Troodon nests, indicating they probably brooded as well (in crocodile nests, a heap of plants provides the required heat).
The geographic distribution of hadrosaur skeletons does not exactly coincide with young hadrosaurs finds. This could mean that hadrosaurs migrated to lay their eggs and make up their nests. They seemingly nested in packs. Similarly, finds of numerous sauropod eggs at the same place seem to indicate that these animals used some particular place to lay their eggs.
The simplest way to estimate intelligence is to compare the size of the brain to the body weight. In the modern fauna, among species of comparable physiology (hence comparable intelligence?), the brain weight grows like the two-third power of the body weight. However, for the dinosaurs which are larger than any living animal, it is difficult to know whether this relation still remains valuable: is it really more complex to understand the images provided by the eyes of a 50-ton-body than those of a 5-ton-body? Moreover, dinosaur weights are not known with much accuracy (the estimation can triple depending on the restoration).
Anyhow, it seems that plant-eating dinosaurs had relatively smaller brains (compared to the two-third power of their body size) than crocodiles: the less brainy dinosaurs were of course sauropods, then the armoured dinosaurs, then the ceratopians. Ornithopods were more brainy than crocodiles. Big theropods were intermediate between crocodiles and birds (with a wide range), and small theropods were probably as 'intelligent' as modern birds or mammals. This ordering is quite normal since a predator needs more complex behaviour than its prey.
Note that these evaluations assign more intelligence to small than to big theropods, whereas small and big forms are sometimes very close among theropods, hence probably had roughly the same intelligence. Thus, how intelligence depends on size is not very clear.
Predatory dinosaurs seem to have had a keen sense of smell, and of limb coordination (they were bipedal and their bodies were narrow). Some theropods seemingly had a good 3D sight. Tyrannosaurs and hadrosaurs had a very good sense of hearing. Hadrosaurs with their crests and sauropods with their high nostrils (and trunks?) would have had a very developed sense of smell.
The cortex, which is in mammals the 'thinking part' of the brain, seems not to have been well developed. However, some birds (e. g. parrots) are quite intelligent without having a big cortex; hence the correspondance is unclear.
Up: Dinosaurs' lifestyles