FLexible UnderPasses (FLUPs) are included in the NAM - no additional download is required. FLUPs consists of underground network puzzle pieces. Car traffic moves below the surface - it's the opposite to elevated road puzzle pieces. You simply plop two or more ramps and connect them with puzzle pieces. The system works also for underground freight traffic, for underground road networks like avenues, one-way roads, streets and RHW, for underground tram routes (including tram-avenue) and for pedestrian tunnels. FLUPs pieces do NOT work correctly for underground rail - please use the special underground rail pieces.
FLexible UnderPasses are usually build on flat terrain and do often cross below other networks (train, road, highway, canals, ...) or parks or custom pieces. It's a fully functional system, the traffic simulator works, UDI can pass and automata work (although they disappear when entering a ramp, they usually appear again at the other end). There is one important drawback, though; you cannot plop lots on top of it.
FLexible
road UnderPasses have existed since the January 2009 NAM. The model of the Marrast road underpass is used as road ramp, but unlike the static Marrast underpass lots, FLUPs are flexible and modular and allow more complex underpasses. The idea for these puzzle pieces also came from the similar rail underground puzzle pieces inside the NAM. FLUPs puzzle pieces can be recognized by their tiny manhole covers at their edges.
FLexible
oneway road and
avenue UnderPasses were included in the June 2009 NAM. You simply plop two or more ramps and connect them with FLUPs puzzle pieces. For the underground connection, you simply plop FLUPs pieces - they work for either road, oneway or avenue underground. The ramps define how the traffic is using the connections.
FLexible
tram and
tram-avenue UnderPasses are included in the May 2010 NAM, using the same system.
NAM version 30 contains one new FLUPs functionality: you can now build
underpass avenue roundabouts.
Here is the link to the tutorial, how to build such FLexible UnderPasses.
Some images - a tram-avenue underpass below rail:

I needed such an underpass in one of my cities, and that's why I started modding in 2007.
An urban area with lack of space:

The avenue passes below the rail (using two straight FLUPs pieces below rail) and two T-junctions connect it to the two road ramps. The tiny manhole covers indicate the subsurface connections.
Caspervg's underpass from
Casper's Portfolio - Update 19: Plymouth's Industry and Residentials - 17th:

The
O'Shaughnessy Tunnel under New Dublin Harbor by jpj_starfleet is a complex functional underpass system:

More examples
(click to increase the image size):

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Bug correction: The underground tram junction under avenue-road junction has faulty paths. Copy the dat file from the attached zip-file into your NAM Plugins sub-folder.