IDs are used to identify certain objects.

They are only unique within the object type, so for example a vehicle may have VehicleID 2009, while a station has StationID 2009 at the same time. Also IDs are assigned arbitrary, you cannot assume them to be consecutive. Also note that some IDs are static and never change, while others are allocated dynamically and might be reused for other objects once they are released. So be careful, which IDs you store for which purpose and whether they stay valid all the time.

type	object	acquired	released	reused
BridgeID	bridge type	introduction (1)	never (1)	no (1)
CargoID	cargo type	game start (1)	never (1)	no (1)
EngineID	engine type	introduction, preview (2)	engines retires (2)	no (2)
GoalID	goal	creation	deletion	yes
GroupID	vehicle group	creation	deletion	yes
IndustryID	industry	construction	closure	yes
IndustryType	industry type	game start (1)	never (1)	no
ObjectType	NewGRF object type	game start (1)	never (1)	no
ScriptErrorType	error message	OpenTTD start (3)	OpenTTD exit	no
SignID	sign	construction	deletion	yes
StationID	station	construction	expiration of 'grey' station sign after deletion	yes
StringID	translatable text	OpenTTD start (3)	OpenTTD exit	no
SubsidyID	subsidy	offer announcement	(offer) expiration	yes
StoryPageID	story page	creation	deletion	yes
StoryPageElementID	story page element	creation	deletion	yes
TileIndex	tile on map	game start	never	no
TownID	town	game start	never	no
VehicleID	vehicle	construction, autorenew, autoreplace	destruction, autorenew, autoreplace	yes

Remarks

(1) in-game changes of newgrfs may reassign/invalidate IDs (will also cause other trouble though).
(2) engine IDs are reassigned/invalidated on changing 'allow multiple newgrf engine sets' (only allowed as long as no vehicles are built).
(3) string/error IDs are only valid during a session, and may be reassigned/invalidated when loading savegames (so you cannot store them).