Are there any known implementations for quantum computing constructs? Quantum Computation is an active area of research that aims to take advantage of quantum physics (e.g. quantum entanglement) to advance the efficiency capabilities of computers (does not alter the Church-Turing thesis).  

What are the most significant experiments that have been conducted to demonstrate quantum-computing theory (such as qubits and teleportation)?
At this stage progress on experimental quantum computing is relatively slow, but there are now a wide variety of systems that can be used to implement one or more qubits. 

At the moment the most developed systems as


Ion traps
Liquid state NMR
Linear optics quantum computing
Superconducting qubits


There has also been a lot of recent work with defects in solid state, solid state NMR, endohedral fullerenes, neutral atom traps, atom chips, etc.

The highest numbers of qubits tend to be in ion traps and NMR, though linear optics is doing well too. 

As regards significant experiments, that really depends what constitutes progress to you. There was a very nice experiment back in 2007 where two separate ion traps were coupled optically, and some nice recent work on segmented ion traps, which demonstrate ways of scaling ion trap computation beyond 10 or so qubits. There has also been some very nice implementations of measurement based computation using optics, which is also important for scalability. If you have a better idea of the type of experiments you have in mind it would make the task of answering much easier.

The US quantum computing roadmap, available here, provides an excellent, though slightly dated overview of the state of the art circa 2004.