I think the answer is they are required for an earth like planet...extended periods without ice? most definitely...but to completely eliminate it, you need a way to explain several occurrences:
Maunder Minimum. In 1645, our sun went through a cold spell where the number of sunspots fell to a low, including 0 for several years in a row. This activity, or rather lack of activity, threw earth into a mini ice age. It's likely that the Maunder Minimum is a far reaching cycle, and much more 'reduced periods of activity' have occurred through our suns life cycle. So you pretty much have to assume the sun is constant for no ice ages to occur, and I think we already know better than to think our sun isn't readily changing year to year.
Asteroid and volcanic activity. Any large scale impacts or eruptions will bring along a nuclear winter type scenario where the globe will experience at very minimum a mini-ice age. An young planet formed when the galaxy was much older might be more insulated from asteroid impacts? A hyper active tectonic plate system might prevent large eruptions from occurring by using the energy that would create a volcanic eruption and relocate the plates with that energy instead? Not sure how realistic any of this is.
It is possible to take a period in the Earths existence and say that there wasn't any ice ages in that period...but it's near impossible to say that an earth like globe would never have an ice age.
Lacking an ice age will have a few key changes on your globe...I doubt something like the grand canyon could actually form without the influence of glaciers. Your land will be much more rugged and lack the soft sedimentary layers that glaciers can cause. It's possible that your terrain will completely lack extended flat plains.
if it is realistic that an Ice Age does not occur, how would that impact the flora and fauna of the planet?
Realism aside...ice age's are one of the key attributes that forces evolutionary change on a greater scale. Ice age's kill...it's an event that operates on a global scale and can be responsible for great stresses to be put on entire species. A global flood brought on by melting glaciers is what possibly eliminated all large species on the North American continent. So without them...
Bigger creatures. Mass climate change is the extinction force on large creatures...small can adapt faster. Without ice ages, large creatures would continue to get larger over longer periods of time
More diversity within species. Same as above...ice ages for extinction and reduce the earth to the species that can survive an ice age. No mass extinction event, more genetic lines of the same specie surviving, more inter-specie diversity.
lack of mammals? Lets face it, warm blooded may never dominate if the extinction force on cold blooded creatures never came to bear. Without an extended ice age, why would warm blooded creatures come to dominate the globe?