Electronic – SPICE Simulator at Linux

There where some algorithms to automatically draw schematics from netlists. This was a (not very big) research topic around the 80.

That said I do not believe there are practical systems available using the result of that research.

I wonder if dot from GraphViz could be used for such quick verification tasks.

I would say that depends heavily on what you need it for. Often the expensive spices are part of some e.g PCB design tool. I'm just trying out MultiSIm from NI (expensive orcad type tool), and it has lots of pretty virtual instruments (e.g scope, distortion analyser, etc) and monte carlo analysis (which LTspice does not have a "convenient" version of - it does have some functions you can use though as Vlad points out, here is a link on using them) but to be honest I find that 99% of things I could do on LTspice.
I find the LTspice setup is by far the quickest out of any spice I have tried, once you get used to the key commands. R for resistor, D for diode, is much easier than clicking the picture (or even selecting from a pop up box in MultiSims case, arghh) and dragging to the right place every time.
You can have a circuit done in seconds this way.

The manual is not as pretty either, but all the info you need is there regarding how to use, eg. the .param, .step and .measure commands for doing things like running an analysis many times and varying parameters. I just tried to run a transfer function analysis in MultiSim in this manner (i.e. run may times and vary a parameter then plot results) but despite reading/wrestling for hours with it, I couldn't manage it, but a quick addition of .step V2 -15 15 1 to the sheet made it possible in LTspice.
I'm sure some of the above is simply as I'm new to MultiSim, and no doubt I am missing something (as the above example simply must be possible in a tool like that) and no I don't work for LT :-) but it has been the only spice that I have used regularly for the last few years. The main point is that it will do all the normal stuff as good (and probably faster) than the expensive tools, but if you need the extras (e.g. monte carle, PCB level anaysis based on actual routing/IBIS models - Altium does this excellently) and all wrapped up in one design tool then you may need more than if can offer.
In my view it can't hurt much to have around even if you do need a more powerful tool anyway.