As Suralle pointed out, ships don't really have to bump into mines. 'Dumb' explosives are obselete in modern militaries today, let alone 200 years from now. It's not really reasonable to suggest that interstellar combat, in which two ships find each other in a cubic lightyear of space, and then quickly match velocities, is possible - but a ship would never encounter one of trillions of mines lurking in that same cubic lightyear. Both concepts are abstract, and if a ship can find its enemy, so can a powered mine.
I envision a few types of mines:
1) Nanomines. Depending on miniaturization tech, these could range from the size of a golf ball (30mm dia) to the size of a BB (4.5mm dia), with a 100mg antimatter charge. With a passive sensors and laser propulsion (no drive mass other than photons, which is more mass-efficient that an ion drive) they could interdict ships using the low acceleration of a laser drive, if they spot them far enough in advance. A mine the size of a BB does not sound powerful, but 100mg of antimatter would easily destroy any ocean ship Earth has ever seen. And a 100-kT cargo ship could carry and drop 200,000,000,000 of them per mission... The most modern antipersonnel mines are often airplane-dropped, the size of a deck of cards, and include electonics to handle arming and disarming (after a set number of years, or when a signal is broadcast). I have not seen any mobile land mines yet though
2) Sleeper Missiles. Similar to those discussed earlier in the thread, these "mines" are really just normal ship missiles modified for extremely long range and fitted with some passive sensors. When an enemy ship is detected, the missile launches itself. These are much simpler (technologically) and more powerful than nanomines, and much more likely to attack a ship (per mine, given their vastly increased attack range and detonation radius), but much more expensive per mine - you could probably only lay one millionth as many.
3) Laser Mines. Imagine a highly-charged capacitor, in which the dielectric is a lasing medium, and one of the charge plates is a mostly-reflective mirror, with an attached columnating lens. Essentially, a laser tube that doubles as a capcitor. With an attached sensor pod, attitude jets (compressed air, a hypergolic fluid as used on the Space Shuttle, or tiny ion drives), and a targeting computer, this mine waits until it senses an enemy ship within effective range, then reorients itself and fires a single laser beam... and then it is dead (energy supply used up) and fires a scuttling charge. Ships enroute don't travel in zigzags, they just accelerate in a straight line until the halfway point and then decelerate... and lasers don't attenuate in space... so these could hit any enemy ship within the sensor range as long as they shoot straight and the target does not change course or take evasive action.
How would these make the game more fun? Well... they add possiblities. An evil, warlike race has no reason to develop mines, as they suck resources and research and cannot be used aggressively. A good race really shouldn't, lest they kill innocents by mistake. Peaceful neutrals, isolationists, and minors would benefit greatly. Minefields are not impenetrable. If you lay them thinly, fleets can go right through them; if they are too low-tech, they will be spotted and evaded or destroyed; if they are too weak, the enemy ships will be hit and undamaged. Mines are more like corporate "poison pills", or the bitter taste of milkweed (and monarch butterflies), or a car with "the club" on the steering wheel - you can buy out a company with a "poison pill", or eat a monarch butterfly, or steal a car with "the club", but why not pick on their much tastier neighbor instead? Minefields mean the attacker will have to accept more losses OR have to invest in point-defense and/or sensors and/or minesweeping ships. The defender has to do additional research and spend large amounts of money on minefields that can never be used offensively, never stop a determined attacker, and never engage the target they want (e.g. a minefield near Mars cannot be used to reinforce Earth).
The way I envision minefields working:
Minelaying ships can lay mines at a certain rate in a square, which increases the number of mines in the square. There is some monetary cost per mine (or per X mines) so that a minlayer set to "Lay Mines" costs money to operate, while a minelayer moving or idling is free. Any ship moving through the minefield may be hit and damaged (or even destroyed) by any number of mines. The number of mines that target a ship is a function of the size of the ship and the number of mines in the sector. These mines may or may not hit, depending on the ship's size, speed, sensors, weapons (maybe it can shoot them), and point defense/chaff. Every mine that targets a ship, whether it hits or not, is removed from the minefield. In other words, ships going through a minefield deplete the minefield somewhat, and may be damaged.
Minesweepers, on the other hand, never get hit by mines, and can clear "X" mines per turn (for free) in a mined square, until they are all gone.
So - I
think it would be fun. Depending on the (money, time, and research) cost and effectiveness of mines and minesweeping, they could have major, moderate, minor, or zero impact on the game - somewhere between moderate and minor seems appropriate. But I certainly think they would add a fun strategic consideration, and economic as well if mined space can kill trade minifreighters - this could be used offensively, or even be an economic penalty to the isolationist approach of surrounding your capitol with minefields.