The Typhoon was supposed to be operational in 2000, hence the hame "Eurofighter 2000".
The German government requested a redesign of several features to meet the needs of a post-cold war Luftwaffe, which resulted in substantial delay. Not only that, but there have been significant cost overruns as a result. The UK is dragging it's heels on it's original procurement of 230+ Typhoons which look set to be cut in the defence review. Fortunately, the Greek air force look set to purchase Typhoons and Eurofighter consortium are trying to sell to air forces around the world.
The original BAe EAP demostrator, upon which the Typhoon was based first flew in 1986.
Meanwhile, the US are also experiencing delays with their F22 Raptor programme. The YF22 first flew in 1990 and is entering service about now with controversy over the original USAF order for 600+ Raptors. It looks unlikely that the USAF will receive more than 300, thus pushing the unit cost higher (as in the case of the Typhoon). It's also unlikely that the Raptor will be as extensively marketed overseas as it's F15 predecessor, given the nature of the technology involved.
The Lockheed / BAe JSF (F35) is slated for a 2012 in service date, but that looks optimistic given the delays faced by other projects. The aircraft is also gaining weight rapidly, which is far from ideal given the weight constraints of carrier operations. The Royal Navy is also expected to get two new large carriers during the next decade, specially designed for JSF operations.
