I am trying to build a simple transformer simulation in LTSpice but my rectifier bridge is giving me negative voltages as well as positive voltages. Also, I am getting half the amplitude of inductor voltage after the bridge (not sure if it is supposed to happen). Here is my circuit schematic. Can you point out what I am doing wrong here?

 

Try this:
Disconnect d2 catode and d4 from ground.
Disconnect L2 from the ground too.

Connect L2 to d2 catode and d4 anode.
Connect d1 and d2 anodes to ground.
Test now.

 

Thanks, my circuit works now. But I noticed something odd. There is high amount of current passing through L1 even if there isn't any load
on DC side of things. I think it is not right because it would mean all adapters would draw too much current even if there isn't anything connected to them.

 

I don't use LTSPICE, but you should also remove L1 and the '-' side of V1 from ground and connect them directly together.

Linear power supplies are VERY inefficient, as compared to switchmode supplies, but this may be a factor of trying to simulate the transformer with air core inductors sans iron core to provide enhanced coupling between the two. 12 A peaks are a bit out of bounds with no load connected.

I take it that you have no transformer component model to work with?

 

Try to increase inductances. And put a load. Open circuits could confuse the simulator too.

 

There is high amount of current passing through L1 even if there isn't any load

Of course there is.
You have a primary inductance of only 100mH (why did you select that value?), which has a reactive impedance of 37.7Ω at 60Hz, giving a magnetizing current of 6.37Apk for a 240Vac peak input (as the sim shows).
Typically, power transformers have a primary inductance in the several Henry range to give a low magnetizing current.