A Student Showcase nominee at the '08 Independent Games Festival, Mayhem Intergalatic is a fast-playing space conquest game. My first thought was "Risk clone," but it isn't actually; although combat seems to be per the Risk combat algorithm, there's no concept of adjacency (any ship can move anywhere on the map, though trips to distant stars can take multiple turns), there are no cards, and a fleet can only make one attack per turn.
What it really is, is "4X lite"; your only real actions are dispatching ships to target systems, and upgrading your shipyards. Basically, upgrading a system's shipyards increases the number of ships it produces each turn, but doing so forgoes one turn of production.
The fact that there are only two actions does mean there's not a huge degree of strategic depth here (and indeed, in common with many similar games, Mayhem Intergalactic suffers from the snowball effect -- success breeds more success, and the end-game is just mopping up). But the simplicity has virtues, too: the UI is extremely intuitive and anyone should be able just to pick up the game and play; and it makes for a fast-playing game (on a small map, less than 10 minutes for a complete game). There is one clever feature in the single-player game; by default, the AI starts off very dumb, but its smartness gets cranked up each time you win, so there is a feeling of increasing difficulty over time.
Where Mayhem Intergalactic works best, however, is in the multiplayer game -- chat is supported, and once diplomacy and alliances (implicit -- no explicit in-game support for such) come into play, it's much more interesting. In the single-player game, it's just a matter of grinding out a win against AIs who don't cooperate; in a multiplayer game, the leader can expect to see the opposition working against him unless he can persuade them otherwise, and that leads to a far more interesting dynamic. Multiplayer games are both via LAN and the Internet; Inventive Dingo runs a dedicated server, but don't expect to find a lot of people there waiting for a game (I assume distribution is limited so far). Of course, you can email your friends and set up a time to play, if you like.
The demo is pretty full featured -- the only limits are that you can't change options, can't save games (no big issue as games are short), can't use custom maps, and multiplayer games are time limited. At $18.95, I'm not sure it's worth upgrading to the full game (at $10, I'd be more sanguine), but the demo is full featured enough to be worth downloading and playing regardless, if this is the sort of game that appeals to you. Nothing hugely creative here, but a nice, smooth implementation of a classic style.