Freshwater is drinkable water, which makes it valuable to cultures as well as plants and creatures. Even in non-desert conditions, drinkable water is often a protected resource. Secure locations, fortresses, etc. which have there own water source are more resistant to siege and less vulnerable to poisoning. A natural source of freshwater can also be healthier, when you don't have sanitation plants. However, historically speaking, freshwater was not always treated as a valuable resource. Often, rivers were used as dumping ground for all kinds of horrible things and could as often be a source of disease, especially in urban areas.
Even the oceans require freshwater if they're to sustain life. Without the influx of freshwater, the water of the ocean would evaporate, leaving its saline content behind and increasing the saline concentration to levels in which fish and many other sea creatures could not survive. Animals often migrate, following the water supply, and humans have often followed those animals. In addition, humans tend to congregate around water, just as other animals do. Sometimes it's the saltwater of the ocean, but equally they choose to live on the banks of lakes and rivers. There are several advantages to this setup. Not only does it provide a supply of freshwater, but there is a supply of all the creatures which live in that water, all the creatures which visit that water, and a ready means of transportation and trade.
Rain itself is a source of freshwater, replenishing lakes and ponds and rivers. However it can also be collected by humans, and if the supply is steady enough a culture can support itself by precipitation. However, rain is somewhat unpredictable. There are dry years, and a culture's demand often outstrips their supply. Lakes and ponds are, essentially, natural storage containers for freshwater and more reliable than precipitation alone.
Your cultures' views on their water sources can play a large part in worldbuilding, but first let's consider the sources of freshwater: ponds, lakes, streams, rivers, wetlands, springs--hot or not--snowmelt and rain.
Ponds and Lakes
Ponds can be small or large, however they tend to dry up for at least some of the year. The amount of different species found within a pond or lake is often dependent on how much contact it's had with other bodies of water. Some lakes (such as Lake Victoria) have changed size and shape and throughout the centuries have connected, disconnected, and reconnected with other lakes or bodies of water, making them diverse in the species they contain. Others have had little connection to other bodies of water and so contain a limited number of species, some of which may be highly adapted to that particular environment. Isolation creates specialization, while inter-body contact creates diversity.
Rivers most often originate in mountains, either from a spring or where rain and snowmelt run down and gather, growing as small streams collect into larger ones, which collect to form rivers. Most rivers end when they hit another body of water, be that a lake or the ocean or another river. Some rivers originate from lakes. Some rivers carve paths for themselves, while others veer around obstructions creating winding waterways and switchbacks. This is often a product of a lack of momentum. Rivers become slower moving toward their middles, or when they encounter certain conditions, making them less able to press through obstacles and more likely to simply go around.
A river's velocity is affected by three factors: river gradient, channel roughness and channel shape. Gradient is obvious, the steeper the slope of a river, the faster it will go. Channel roughness refers to the river's bed. A rough bed--say one strewn with boulders or littered with large amounts organic matter--generates more friction and slows the river down. Channel shape is along the same lines. Basically, it means that the more water that is in contact with its bed, the more friction there is, the slower the river. So, all other factors being equal, a wider, shallower river will move more slowly than a deep, narrow one.
Cultural and Worldbuilding Implications
Animals need drinkable water as much as people do, and so they tend to congregate around it, or to migrate from one source to another. This affects the circumstances of your culture in many ways, from which animals they have to eat seasonally to which animals they have to defend against. If there are a lot of different types of fish and mussels and such, they may not eat many land animals, or may eat them only at certain times of the year. Because of the troubles of transporting food over long distances, what's available fresh will be more common than what is not. And less expensive in general, although there are probably rare or expensive local foods as well, of course.
Water is also a big factor when it comes to trade. It's easier to move products, especially heavy products, over water. (Although it can be just as dangerous.) Boats can transport larger loads, more quickly, with need of fewer animals that need to be fed and cared for. Transporting people is easier by boat, and depending on the engineering skills of your particular people, canals and dams can create easily traveled waterways.
Waterways can also serve as protection. It's harder for sappers to get at the walls of your city if you've got water on some or all of its sides. It's hard to get soldiers to it as well, and sieging such a city requires a naval strategy as well as a land-based one. Depending on how wide the water is, catapults and ballista may have trouble getting within range, and defenders can be concentrated in areas the water doesn't protect as well. (Of course, history is full of people smart enough to find their way around the water, and the lack of defenders could turn into a city's downfall.)
Rivers and lakes make also serve as boundaries. This side is ours and that side is yours, but controlling the banks of a river or lake can also be a reason for fighting. If a particularly important resource comes from just one lake, whoever controls the banks controls the spice... er, I mean the resource. ;-)
It pays to consider the impact your freshwater sources have on your peoples and cultures, and how you can best use them in your worldbuilding and even your story itself.