A River is not alive in the usually sense of the word which is properly restricted to bonafide "living" systems. Poetically however it is sometimes useful to use a metaphor and think of an inanimate but complex system as being 'alive'. This is useful analogy because some natural systems are very complex and so are living systems. A river is a complex system because it responds to external perturbations (minor upsets) in complex ways. For example, if one dumps a lot of sand into a river, the river will change its course over time in such a way as to come back to an equilibrium (stable) configuration. This is similar to for example the way the internal processes within your body regulate the temperature: when its hot out you sweat and evaporation of sweat tends to cool you. If its cold out you get goose bumps and your blood circulation slows down to conserve your body heat. This sort of SELF-REGULATION is common in COMPLEX systems.

A river is a geological entity but it also hosts many life forms all of which are interrelated.

Defining life is not an easy, but generally, most biologists would say "no", a river is not alive.

Like living things, rivers represent a flow of material, in this case water, through them, just as much of the matter in living organisms flows through them. Rivers also tend to concentrate matter that had been widely distributed into a more narrow place, thus (locally) destroying entropy and creating order (although, like life, they need an external source of energy and externally created entropy, namely the Sun's light and the Earth's gravity, to do this).

However, this really isn't a quintessential aspect of life; wood, for example, is made up of toxins created by a plant's metabolism that have been sequestered where they cannot do it any harm, and provide support on the side. The material in wood doesn't leave normally until after the plant is dead.

Moreover, rivers (1) do not reproduce, (2) do not store information of the design of their form within them, and (3) possess no internal organization and form except that which gravity and the laws of fluid mechanics dictate.

Life forms, while they conform to the laws of physics, they store information which physics then regulates by means of differential reproduction of different packages of stored information, i.e. evolution by natural selection.

Rivers evolve:
They change over time as a result of changes in climate, changes in the geology/topography from uplift of mountains, they change from presence and absence of vegetation.
Rivers also grow:
They start as a small stream, and grow, cutting through the soil and rocks, growing until they ultimately reach the ocean at the height of their maturity.

Do you think a river is alive? Why or why not? Do you think living things live in rivers? I'm guessing your answer is: yes, because fish live in rivers.

Where exactly does a river begin and end? Where exactly are the sides of a river? Do you know of any living thing that doesn't have clear borders and some kind of skin or shell that keeps some things in and some things out? Does a river have this?

Sometimes people talk about "living water" because water gives life to every living thing. But a river is not alive, scientifically. Some words have special meanings in science. For example scientists call some vegetables "fruits" because they have seeds. So scientists say tomatoes and squash are fruits.

Scientists (and actually, everyone) have struggled since the dawn of history trying to pin down exactly what "life" is, and where to put the line between life and non-life. There's still no perfect answer, since things like complex viruses or specialized computer programs still tend to muddy the waters. In any case, there are some fairly rigorous definitions that exist, which define life as something that possesses the following six traits:

1. Homeostasis: Maintaining a consistent internal state (like sweating to maintain our temperature)
2. Metabolism: Require energy and gain it by utilization of compounds in the environment
3. Growth (not simply the addition of random matter, but extension of the organized form)
4. Response to the environment (like a plant turning to face a light)
5. Adaptation: The ability to change behavior or activity in response to signals and stimuli.
6. Reproduction

Under these rough definitions, a river does not satisfy 1-- its level may rise and fall over the year, and it does not maintain in level or temperature. It doesn't fulfill 2 either. It does fulfill 3-- a river can get bigger over time, reaching new areas and splitting into new tributaries. It also fulfills 4, since it can bend around a boulder in its path over time. You might argue that it fulfills as well, since in curving around the path, it etches out a new path which it will stay with, even if the boulder is removed. It fails 6 as well, since rivers don't make new rivers.

It's worth noting that some books will list very specific traits (such as being made of cells) as characteristics of life-- but those definitions have gotten too narrow. If we tomorrow discovered a form of life based on, say, complex clay-mineral substrates- either deep underground or on another planet, they would exclude it as life by an arbitrary claim that all life is cellular life. As I stated at the beginning-- pinning down life is tricky.