In some cases, it may be desirable to be able to connect bare, unterminated wire to a circuit. Screw terminals provide a good solution for this. They are also good for situations in which a connection should be capable of supporting multiple different connecting devices.
The downside of screw terminals is that they can come undone fairly easily, leaving a bare wire waving around in your circuit. A small dab of hot glue can address this without being too difficult to remove later.
Screw terminals are typically designed for a narrow range of wire gauges, and wires that are too small can be as big a problem as wires that are too big. SparkFun carries two types of screw terminal--a .1" pitch version and a 3.5mm version. Most screw terminals are highly modular, and they can easily be extended at the same pitch by simply connecting two or more smaller sections together.
Most pieces of power test equipment (multimeters, power supplies) have a very simple connector called a "banana jack" on it. These mate to "banana plugs", crimped, sprung metal plugs, meant to make a single power connection. They are frequently available in a stackable configuration and can be easily connected to any type of wire. They are capable of carrying several amps of current and are inexpensive.
Named for obvious reasons, alligator clips are good for test connections to posts or bare wires. They tend to be bulky, easily cause shorts to nearby bare metal, and have a reasonably poor grip that can be easily compromised. They are primarily used for low-cost connections during debugging.
IC Clip (or IC Hook)
For more delicate probing operations, there are a variety of IC clips on the market. These are sized to allow a user to clip them onto the pins of an IC without contacting adjacent pins; some of them are delicate enough to be clipped onto even fine-pitched SMD component legs. These smaller clips can be found on logic analyzers as well as test leads, which are great for prototyping or troubleshooting circuits.