Is there a time limit in The Ur-Quan Masters?
TL;DR and nonspoilered: YES, but it's a very large limit so there's no real need to rush.
Full answer in spoilers. LOTS AND LOTS OF SPOILERS.
The backdrop of the game is the brief lull in the galactic conflict as the green Ur-Quan (the Kzer-Za) have finished conquering their assigned chunk of the galaxy while the Black Ur-Quan (Kor-Ah) have finished eradicating all sentient life from their chunk, and now they've met halfway to fight each other in a contest they call Supremacy of Doctrine to see which of the two approaches should be adopted for the entire galaxy.
Unfortunately
for everyone that's not Ur-Quan, the Kzer-Za ran into some unexpectedly heavy trouble in this sector of the galaxy from the Alliance of Free Races and it looks like the Kor-Ah are going to win this one. There are a few things you can find out and do that will delay their victory even further, but ultimately unless you beat the game they will eventually win and take their prize, the Precursor Superdreadnought Sa-Matra, and eradicate every sentient species in the sector.
Once that happens,
you're on the final time limit -- since every eradicated species will no longer be in a position to prevent you from picking up the various necessary MacGuffins you can still rush a Pyrrhic victory, but once they destroy the Chenjesu Homeworld before you can evolve them into the Chmrr, you're screwed.
As it happens,
Chenjesu is the last stop on their Sectorwide Genocide Tour, so after that they double back to nuke the starbase over Earth and send a message probe to taunt you
... which is the Non-Standard Game Over.
ETA: According to this link (Spoiler warning) you have roughly 4.5 in-game years before the clock starts ticking to failure; time passes at a rate of one day every thirty seconds in interplanetary space and one day every five seconds in hyperspace/SPOILERSPACE. (Thanks to Kaffeleif for the addendum)
As Shadur mentioned, there is a timelimit. Depending on various factors this limit is set to 4.5-5.5 years of ingame time.
These factors are
* If you sent Utwig and Supox to fight Kohr-Ah you get 1 extra year.
* If you are in the Delta Crateris solar system when Korh-Ah wins their war you get 7 days extra
* The Korh-Ah will travel to other races ships and destroy them. Depending on where these ships are you can gain some extra time
Source: http://wiki.uqm.stack.nl/Star_Control_II_facts#Star_Control_II_fact_.235_-_Timed_events Under the block "Korh-Ah events"
Strictly speaking, yes there is a time limit... (spoiler warning) The game is intelligently written and scripted to respond interactively to the decisions made by the player. You may play nice and fall into the role of The One, or you can be a bit of a jerk. Your decisions may cause certain other races to leave our galaxy, or may cause the destruction and extermination of another race, and much more. Its part of the rich story telling aspect of the game which is the best part for me imho. But these are subplots and doesn't affect the main plot. Which means they're more like timed events served to advance the story. So you should be disappointed if you are expecting multiple story endings like Fallout. As i said the timer feature still applies, but the good news is that almost in any style of game play, you shall find more than enough time to complete the mission. Now, go play this epic game and enjoy. (p.s. I will take a minute of vigil tonight in memory of the atrocity of Activision in its brutal killing of such an esteemed title.)