Some depictions of Rams are more accurate than others, though it is difficult to mess up showing a log being slammed into a wall.

Suspended or hand carried rams were both used in history. They were effective due to material in fortifications, stone and brick especially, not having a propensity to flex. This leads to the material cracking and breaking when struck with a large heavy object moving with substantial velocity. So, not much to get wrong with execution.

The ram would be replaced by the Cannon as the main breaching tool, however, around 1374, when they are first recorded as having breached a wall in Europe.

Siege towers, are also pretty straight forward, but they are often shown as dozens of towers lumbering towards their objective. In reality, it was typically between 3 and a dozen towers. These towers were formidible, and often the first targets of a defenders ire. Some towers, such as at the siege of Kenilworth Castle in 1266, could carry 200 archers and numerous catapults. Other examples of towers are basically enclosed ladders for infantry to climb walls in a protected enclosure. Pretty deadly stuff.

The conclusion you can draw from this is that, yes, the examples of siege weaponry are typically accurate, with exceptions made toward dramatic effect in movies and shows.

Edit: With regard to how frequently they were used, they were common in many Sieges. Sieges are expensive to maintain, so attackers look for ways to speed up the surrender of the defending force. Usually the fastest way is to breach the defenders fortification, and rams and towers are the way it was done for a very large chunk of human history.

Examples of siege engines in use include, but are not limited to: Siege of Rhodes, 305 BC Siege of Jerusalem, AD 70 Siege of Rome, AD 408-410 Siege of Acre, AD 1103 Siege of Bayonne, AD 1130-1131 Siege of Jerusalem, AD 1152 Siege of Kenilworth, AD 1266

For the Siege of Jerusalem that u/SwordOfAmmonx1 alluded to in 1099, the crusaders spent three weeks building a siege tower. That seems kind of counterintuitive, right? The defenders inside the city were watching them (and attacking them) the entire time, and in the end, there’s a big siege tower right in front of them, and the Muslims in Jerusalem know exactly where it is and where it’s going. How could that possibly help?

But the night before the final day of the siege, somehow the Muslim defenders weren’t paying attention, and the crusaders disassembled the entire tower, carried it one kilometre away, and rebuilt it in front of a less well-defended part of the wall. Still, after that it took the entire day to roll the tower up against the wall, so the surprise was kind of short-lived.

The crusaders also built a huge battering ram, which broke down part of the wall, but then the Muslims poured burning oil on it and set it on fire. The crusaders actually used this to their advantage, since the fire destroyed the ram, left a hole in the wall, and left room for their siege tower to be moved up toward the hole.

“This three-storey structure, some sixteen metres in height and filled with men - including, on the top floor, Godfrey of Bouillon himself - was immensely heavy, slow-moving and unwieldy. Moving the tower up to the walls was a hazardous process because once in range of the Fatimid mangonels its ponderous bulk presented a perfect target. One Latin chronicler noted: 'The Saracens defended themselves from the Franks and, with slings, hurled firebrands dipped in oil and grease at the tower and at the soldiers who were in it. Thereafter death was present and sudden for many on both sides.'

…The first stage of the siege tower's deployment was essentially a slow but deadly race, in which the defenders sought to destroy the structure with every missile they could muster, and the crusaders pushed on as fast as possible, hoping to slip under the curtain of fire. This was a high-risk manoeuvre, and at one point during the advance Godfrey was nearly killed: 'A stone flying randomly hit a certain soldier who was standing at [Godfrey's] side hard on the head. His skull was broken and his neck shattered and he was killed instantly.’

…The wattle screens tied around the structure managed to deflect many of the Fatimids' stone missiles, and the defenders had no better luck using fire: 'From time to time they hurled on to the panels protecting the engine pots vomiting flames . . . [but they] were covered with slippery skins and did not hold the flames or live coals thrown onto them, but at once the fire slipped from the skins, fell to the ground and went out.’

…The immense height of the siege tower now gave the Franks a significant advantage - at this point the main city walls were about fourteen metres high - allowing Godfrey and his men in the top storey to rain down a stream of suppressing fire upon the defenders. In desperation, with the tower now perhaps less than a metre from the walls, the Fatimids deployed a 'secret' weapon. They unleashed a peculiar form of flammable missile, akin to Greek fire, that produced a flame 'which could not be put out by water', hoping that this finally would burn the siege engine to the ground. Luckily for the crusaders, local eastern Christians - presumably those exiled from Jerusalem - had forewarned them of this mysterious fire and revealed how to deal with it. Although impervious to water, the fire could be extinguished by vinegar, and so, having shrewdly stored a supply in wineskins inside the tower, the Franks countered the attack almost immediately."

Eventually they made it onto the wall. The tower had a rough bridge that could be lowered so that the crusaders could simply walk across (well, as simply as possible given that there was a big fire and people trying to kill them on the other side)

There were only two siege towers here, not like movie depictions where there's an endless line of towers. The other one on the opposite side of the city was destroyed by fire:

"'First we began to push our [tower] against the walls and then all the hellish din of battle broke loose; from all parts stones hurled from [catapults] flew through the air and arrows pelted like hail ... As the machines [of war] came close to the walls defenders rained down upon the Christians stones, arrows, flaming wood and straw, and threw mallets of wood wrapped with ignited pitch, wax and sulphur, tow, and rags on the machines…The mallets were fastened with nails so that they stuck in whatever part they hit and then burned.'"

Quotes are from Thomas Asbridge, The First Crusade: A New History (Oxford University Press, 2004), pg. 310-316.

Another example is Emperor Frederick I's siege of Crema in Italy in 1159. He had a battering ram, but just one siege tower:

"Frederick ordered hostages attached to the upper floors and even had lit candles placed in their hands at night in the expectation that the defenders would not kill their own people; but the desperate Cremans continued even though some of the hostages were severely wounded or killed. Frederick had the tower withdrawn, perhaps because of his lack of success or because, maybe, even he was repelled by the barbarity."

(John B. Freed, Frederick Barbarossa: A Prince and the Myth (Yale University Press, 2016), pg. 247.)

So they were used pretty often, but it took an enormous amount of resources just to build one or two, and using one could be pretty gruesome for the people inside.