Minefields are your friend.

In general it can be said about a game that "if you are not laying minefields, you are losing".  Here are some tips about them.

Against Cloakers
Minefields are your best defense against cloaking races.  (Except for the fascists who have glory devices)  With few exceptions, all cloaking ships hitting a mine will be damaged enough that it will not be able to cloak.  Once they cannot cloak, the advantage that race has over you is gone. (well, with a really good player, diminished ;-).
They are especially effective against the Privateers, who (in a registered game) will be flying 162 LY  per turn.  Since the chance
of a ship hitting a mine is 1% per LY travelled...*cumulative*, any ship flying through 100LY of mine will hit a mine 100% of the time.  Boom.

Optimize
Optimize your torpedoes for your mine-laying ships.  How do you optimize them, one might ask.  The answer is "it depends on what you have lots of, and what you're short of".  "The Firm" document gives a good table of torpedo cost breakdowns.  If you have money coming out of your ass, but no minerals, you want to use Mark 8 torpedoes to make minefields, as they give you the least amount of minerals used per mine.  Conversely, if you have lots of minerals, but moderate money, Mark 7 torpedoes optimize for least money used per mine.  However, remember that at the same time, you may be optimizing for the size of your cargo hold.  In a small cargo hold, bigger torpedoes equates to more mines laid.

Many small, few big
Build many small minefields instead of a few big ones.  Big minefields are much easier to destroy than a bunch of little ones.  Also, the bigger the minefield gets, the more resources you are spending to incrementally increase the radius of the minefield.  One big minefield, for the same resources, could make four minefields half its size.  Further, if you plan their sizes accordingly such that the edges don't cross the centre (i believe that's how it works) of the neighboring minefields, you can overlap minefields!!!  That is, somebody flying through the overlap zone has increased chance of hitting a mine, as per the table, below.  Generally you have some ships dedicated for this purpose that fly around dropping a set number of torpedoes, then fly to the next location to drop another set number, eventually creating a giant wasteland of overlapping minefields.

For overlapping minefields, here is a table that will demonstrate the advantages that overlapping minefields will bring you (or hardships that you will face while flying through one).  This table includes relevant distances for flying around in warp well areas, all the semi-useful and useful engine tech distances, including the Privateer doubled distance, and a few number just to fill in data.  This uses the same equation as the Crystal web mine proof, except using chance to hit per LY as 1% instead of 5%.  The table assumes that the entire distance is travelled in the overlapping minefield area, which is usually not the case.
 

Destruction
You can destroy your enemy's minefield by dropping your mines on top/close to it.  When minefields of enemies overlap yours, they destroy each other until they no longer overlap.  If you have lots of resources for torpedos/mines, but not many ships available for minefield clearing, this is an extremely fast (but costly!) way to clear enemy minefields, especially when they're a bunch of little ones, as described above.

Minimal minerals
If you are short on minerals and long on time, you can use a nonlinearity in the game to create lower tech torpedoes for less than the usual mineral requirements.   In this situation, you lay a big minefield of Mark 8 torpedoes (make sure you're not interfering with your other permanent minefields), and in the next turn, use a ship with lesser torps (say, Mark 4) to scoop mines and create torpedoes.  In the case of Mark 8 -> Mark 4, you can make Mark 4 torpedoes for approximately 1/3 the mineral cost using this method.

Carry money
It is a good plan to always carry money on the mine-laying ships (if you have it) so that they can restock with minerals from distant planets and build more torpedoes in space.

Web mines
Crystal web mines are pretty straight forward - avoid them!  (If you're not the Crystals, that is)  A trick i recently learned for the crystals is that they can lay web mines in the name of other races overtop their own web mines *without it destroying* their own web mines.  This is very significant.  If the web mine belongs to another race, it will not sap your fuel, but it will increase your chance of hitting a mine while in that space.  You may think "but then they're open - they lay a minefield that another race can pass through"....but they can just lay ten other minefields in the name of the other races, increasing the chance you'll hit a mine significantly.  Once you hit one of their mines, it will take you longer to get out of the web, and drain more fuel.  (and maybe hit more mines, sucker!)

Remember: In default settings, while the chance to hit a normal mine is 1%/LY cumulative, the chace to hit a Crystal web mine is 5% /LY cumulative!!!!

Throwing a little math at the worst case, if the Crystals overlapped a web mines in the name of every race in the game, your chances of hitting at least one web mine after only travelling one light year is a whopping 40%!  This increases non-linearly, as can be seen in the following table: (proof)
 

Warning
Beware that this information doesn't all apply to the shareware version of the game.  For instance, you cannot mine scoop, drop a specific number of torpedoes, or make torpedoes in space in the shareware version of the game.

Crystals overlapping mines proof:

Chance to hit web mine/LY:          5%
Chance to not hit web mine/LY:    95%

There are 11 races, so if the Crystals lay web mines in the name of each race, this results in 10 web minefields being dangerous to any given race.  (except the Crystals, of course)

Chance to not hit any (overlapped) web mines/LY of the 10 other races = (95%)^10 = 59.9% = 60%

Chance to hit at least 1 web mine/LY:    40%

The equation describing the chance to hit a mine in one turn is as follows:

chance to hit = 1 - (1 - x)^y ; where x is the chance to hit a mine in a single (non-overlapped) web mine in one turn, and y is the number of overlapping minefields.  (in the Crystal web mine case, y = 10)

With these kind of odds, your ship will belong to the Crystals before you can wimper "Tim Continuum"!