Can any jet perform a vertical take off and transition from hovering to forward flight ?

All Harrier variants could do that. So could the Yakovlev 141 but only 4 were ever built.

A number of of VTOL jets have also been built in the past but not in any meaningfully true production capacity.

The F35B/Lightning II cannot usefully perform true vertical take-off. In demonstrations where it carries no armaments and barely any fuel and has been stripped right down to basics it can do it, but in genuine service it’s a short take-off model using vectored thrust and wing lift, and can then hover and land vertically. Vertical landing has to be with very low fuel loads, requiring fuel-dumping before landing if necessary. Otherwise it’s really a short-landing aeroplane which again needs wing lift to help it to land. So it’s really a STOVL (Short Take-Off, Vertical Landing) and not a true VSTOL jet. 

VTOL is not that important these days, but during the Cold War the ability of the Harrier to land and take off vertically from wooded forest clearings requiring no airstrip and not even a short length of road was of critical strategic importance. 

The F35B/Lightning II almost never happened. It was just far too heavy during development and still remains a heavy machine. The Harrier/AV-8 has the massive advantage that a single engine provides all of the lift for VTOL operation and normal forward flight. Every other hovering jet design including the YAK-141 depends on having jet engines devoted solely to vertical operation which then become parasitic dead-weight in normal flight. 

To improve range all Harrier/AV8 variants were usually used in STOVL mode, despite all being fully VSTOL capable.

The above answer ignores the huge number of jet-powered helicopters, and the jet turbine powered V-22 Osprey.

Most cannot.                

Even if they could vector their thrust downwards the answer would be NO.

Most jets cannot develop enough thrust to lift their own weight without substantial forward speed over their wings.

The HARRIER..

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https://en.wikipedia.org/wiki/Harrier_Jump_Jet

Yes.  Every jet that has ever existed and every jet now can take off straight up, hover for a while and then take off forward or even backward and sideways.  Any 9 year old boy knows that.

Only the ones designed to do so.  They have thrust vectoring nozzles/lift fans/lift engines that allows them to take off vertically.  There were a number of VTOL jets built over the years.  Some, like Mirage Balzac V/Mirage IIIV never advanced beyond the prototype stage, others, such as Hawker P.1127/Hawker Siddeley

Kestrel FGA1 went on to be developed into the highly successful Harrier/AV-8 family.

The only jets I know of that can hover are some models of the Harrier (I believe the Hawkey Harrier and Harrier II), the F-35 II, and F-35B. They are able to do so because:

1. They have thrust-vectoring engines that can tilt the engine nozzle vertically.

2. Their thrust-to-weight ratio is greater than 1, depending on how loaded the aircraft is (the F-35 models on MTOW (max takeoff weight) can't vertically takeoff).

The majority of jet engines aren't capable of thrust-vectoring. Some jet engines are capable of thrust-vectoring but can't tilt the engine nozzles vertically such as the engines on the F-22. Many fighter jets have a thrust-to-weight ratio greater than 1 and are capable of flying vertically but can't hover due to the lack of thrust-vectoring engines.

Edit: according to a more recent answer, all Harrier models can do that. I thought only some could.

Also, the V-22 and helicopters with turbine engines aren't considered "jets". They're propelled by rotors powered by turbine engines, but the engines themselves aren't propelling the aircraft.

No.  Planes have to use runways to take off and to land.  Some VTOL jets do exist but they are rare.

Only a VTOL ( Vertical Take Off and Landing ) jet can hover.

All other jets require air to move over the wings to generate lift in order to fly which means it needs forward flight.  Any attempt to hover would cause a stall.

Of course. The Hawker Harrier and the Lockheed Martin F-35. If they couldn't they would not be of much use.