Summary: Injectable drugs are those which can be reasonably injected.
Basic Reasoning
Almost any substance can be prepared in as an injectable solution, but with some it is very unwise. Injecting bleach is a bad idea for obvious reasons-- however with many substances, the reasoning is more subtle.
For example: Most codeine is produced by the methylation of the hydroxyl group of morphine (a minor change). However, injecting codeine can cause facial swelling, pulmonary edema and convulsions (#1).
Definition
Considering this, I posit that injectable drugs are those which meet both the criteria for being drugs (saline solution is not an injectable drug), and can be injected with effects similiar (though possibly of varying intensity) to those of other routes of administration (insufflation, inhalation of vapors, or ingestion)
Several different methods of injection exist: Intravenous (IV), Intramuscular (IM), and Intradermal (subcutaneous, SC).
Advantages/Disadvanges as a method of administration
The advantages of injecting a drug are a rapid onset (IV), no impact to respritory/gastro-intestinal systems (all), and utilization of an extremely high percentage of the drug (all).
Disadvantages include high risk of overdose (all, esp. IV), swelling (all), blistering (SC), soreness (all, esp. IM), track marks (all), holes in your skin (all), acute discomfort (all), scar tissue formed on skin (all), and the dangers associated with injecting substances (see below).
Dangers
Almost all of the dangers of injecting drugs can be avoided with the appropriate medical procedure (like going to a doctor); Proper procedure is easier to follow in theory than on the metaphorical street.
An individual who is not trained in administering injections will almost always cause significant amounts pain, will likely cause excessive amounts of damage to the site (scraping around in the inside of the vein...), runs the risk of collapsing veins (untrained individuals, even if attempting IM injections, run a significant risk of this)
Injecting substances of unknown purity and origin run the risk of dangerous contaminants, either chemical or biological (See: cotton fever).
Needle sharing can result in spreading bloodborne pathogens (AIDS, Hepatitis-- you name it). If for whatever reason someone puts a gun to your head, forcing you to share a needle, at least sterilize it.
"Street drugs" which are frequently injected include heroin, methamphetamine, ketamine, pcp and cocaine.
Sources, Notes
(#1) http://www.erowid.org/pharms/codeine/codeine_faq.shtml