What are the pros and cons of single-engine vs. twin-engine?
In the light aircraft world there are a few trade-offs to consider.  The short version:

Single-Engine Pros:  


Simplicity
One engine means fewer controls, a simpler fuel system, simpler vacuum system, simpler electrical system, etc.
Operational cost
Only one engine to feed, so you spend less on - fuel &amp; oil per flight.
Maintenance cost
Only one engine to maintain - One set of spark plugs &amp; cylinders, One engine to overhaul.


Single-Engine Cons:  


No redundancy: You have one engine, if it fails you're a glider.
Singles generally tend to have less spacious cabins than twins.




Twin-Engine pros:  


Redundancy
If you lose an engine the other will give you a chance to get to a landing site.
Cabin space
If you step up beyond "twin trainers" you can get a very nice cabin in a piston twin.
Equipment
Again, if you step up beyond the "twin trainers" twin-engine planes tend to be "traveling aircraft", so they often come with nice features like deice/anti-ice equipment.  


Twin-Engine cons:  


Operating costs
Two engines to feed (fuel &amp; oil costs double).
Maintenance costs
Two engines mean twice the cylinders, twice the spark plugs, etc.
Complexity
The redundancy you can get in a twin comes at a price: Synchronizing the propellers, a more complex fuel system (crossfeed), paralleling alternators, vacuum system failover, etc.
Short and Soft field performance can be lacking.
Failure of an engine can be problematic. 




In addition to the operational considerations there are some other practical items to consider: twin-engine aircraft require a multi-engine rating (which means more training time). Twins will also generally be more expensive to purchase/rent (and may be more difficult to rent when away from home), and will likely cost more to insure (particularly for low-time pilots).