Can there be acceleration without work? Since $W=Fs$, $F=\frac{W}{s}$. When you substitute this in the formula for acceleration, $a=\frac{F}{m}$, you will get that $a=\frac{W}{ms}$. Then, when work equals zero, acceleration will be zero.
 A: Magnetic forces don't do work on an otherwise free particle because the force is always perpendicular to the velocity. Without using calculus, you have to remember that the work $w=F S$ only when $F$ and $S$ are parallel. More completely, $w=F S \cos(\theta)$ where theta is the angle between $F$ and $S$. In the magnetic case, $\theta=90$ degrees so $\cos\theta=0$ and $w=0$
With calculus, the force is defined as $\vec{F}=q\,\vec{v}\times\vec{B}$ where $\vec{v}$ and $\vec{B}$ are the velocity and magnetic field. A useful fact to know is that the cross product of two vectors will always be perpendicular to the original two vectors. Now calculate the work, $w=\int \vec{F}\cdot d\vec{s} = \int (q\,\vec{v}\times\vec{B})\cdot d\vec{s}$. Recall that $d\vec{s} = \vec{v}\,dt$ so $w=\int (q\,\vec{v}\times\vec{B})\cdot \vec{v}\,dt$. The useful fact above says that the dot product in the integrand is 0 so the work is 0.
A: 
Can there be acceleration without work?

Yes. An object going round in a horizontal circle at constant speed is accelerating because the direction of its velocity is changing. However, the magnitude of its velocity (its speed) is constant, and so its potential and kinetic energy are constant. Therefore it neither does work nor has work done on it. Although there is a force acting on the object (the centripetal force which keeps it moving in a circle) this force is always at right angles to the velocity of the object and so it does no work on the object.
A: The Coriolis force is always orthogonal to the velocity vector so it does not do any work on a fluid parcel it acts on, but it causes acceleration that changes the direction of the velocity vector.
When deriving an equation for the kinetic energy balance (or turbulent kinetic energy balance), the Coriolis term drops out.
A: Yes, there can be acceleration without work.
Consider a particle on a string in uniform circular motion with constant speed.  Since the speed is constant the kinetic energy (KE) is constant.  But due to the centripetal force on the particle from the tension in the string, the particle has acceleration toward the center of the circle.  The work from the tension force is determined by $\vec T \cdot \vec v$ and since $\vec T$ and $\vec v$ are at 90 degrees there is no work.  The velocity vector changes, hence the particle is accelerated; the speed (magnitude of the velocity) is constant, hence the KE is constant and there is not work done on the particle.
A: This depends on the definition of work.
The answers including circular trajectory should also include the mention that acceleration towards center has a change of distance towards the center. Thus, if you define work as force times travelled distance, acceleration towards center also includes work.
However this work is immediately released to the change of motion from linear path.
The discrepancy here is that usually definition of work is taken from linear systems that is not compatible with particles in nonlinear systems. Definition of acceleration and work have to be compatible.
In other words:
No, there cannot be acceleration without work. Otherwise you violate Newton's laws and you get a Nobel price.
A: Simple answer is Gravity.
When a ball dropped from a height, it experienced acceleration without any external work or force acting on it.
A: The fundamental physics principles state that energy does not vanish, it just changes its form. Consider E=mc^2, electromagnetic waves interacting on particles or circular motion.
Work is the change in energy (e.g. difference of potentials energies).
Acceleration is due to the change in velocity and thus change in kinetic energy.
When you have acceleration you increase kinetic energy and this reduces other types of energy (or similar resource). Therefore you cannot have acceleration without work.
Most of the answers claiming that circular motion has acceleration without work are neglecting the fact that the object creating the force at the center is also affected by the object circulating the center (e.g. Moon creates tides on Earth).
The simplest example is a Olympic sport of hammer throwing. The thrower stands straight initially straight. Once there is motion in the hammer, the thrower leans in the opposite direction to gain balance and does work into the system.
For example, a 100kg person is moving his mass by 10 cm to balance the centripetal force of the hammer. Thus, in radial direction only, the hammer thrower has done work W = F.s where F is the horizontal Force component caused by the gravity and the tilt-angle of the thrower and s is the horizontal distance of the tilt. The F equals the centripetal force of the hammer (and the corresponding centripetal acceleration). The work has to come from somewhere. The same applies to all fields (magnetic, gravity, etc.).
No Work, No Acceleration.
Don't believe everything you are told to.
