Troika!

Probably one of my favourite sit down and play RPGS. Troika is insanely fast to learn and GM. It's more than flexible enough to run most of what you can think of in its weird fantasy. The play style of Troika tends to lean more into the improv side of things but unlike most games its actually fairly easy to improv on the fly as a GM. Almost all weird things a player wants to do can be handled with a few roles and making new NPCs and weapons is fast. Not to mention that there are plenty of super high quality short adventures designed for it that can be read in an hour and then ran for easily a few sessions.

Due to its rules light nature there are also plenty of 'Splats' for Troika such as Weird War (you can find an illustrated version here). These kinds of hacks can completely genre bend the system to something entirely new and unique.

Traveller (Mg2e)

Traveller is in my opinion the best answer to star fairing sci-fi. The typical mode of play is jumping from planet to planet, solving problems and taking on suspicious cargo all to pay off your astronomical debt also called a space ship. If you listen to some people you might be led to believe that this is a very complex system to run but the truth is that although it has loads of subsystems and procedures most of them can be ignored fairly easily or introduced slowly into play. Unlike games like D&D or Pathfinder combat is quick and deadly (after all its hard to take a lazer gun to the chest and walk away from it) so the best solution to combat is often to circumvent it or to plan ahead.

If you are on the fence at the very least have a look at travellermap.com its a marvel that plots every single star system currently known in the setting and links with the wiki for all sorts of random tidbits of any given planet.

I also wrote a larger review here.

Dungeon/Mutant Craw Classics

These two systems are really splats of the same system. DCC takes a lot of risk for its artistic vision and it probably wont be for everyone but if you are looking for something like the old school gonzo play it might be for you. The main barrier to entry is its dice, for reasons DCC/MCC use weird dice such as d7s which can be a pain to get a hold of but it is worth it (there are options for playing with the normal polyhedral dice but in my opinion it doesnt work as well). Probably the most inventive systems are its magic system - where every wizard isnt fully in control of their magic and the concept of the "funnel" i.e. an adventure that takes a bunch of level 0 characters and by the end you have 1 or 2 level characters each.

Manapunk

This is a game I have been making for the better part of 5 years. From the setting to the rules ive changed about everything atleast thrice but I think I'm getting somewhere. The core idea is a semi dystopian sci-fi / fantasy setting where mana is a physical resource that has taken a similar place in the economy as oil has to todays world. Players are those that are rising up against the system and doing weird magic while doing so.

Although I have been working on it on and off I have done a play test or two and hope to get something more ready for play in the next year or so but for now it lives as a collection of files on my computer. At the very least I want to get an SRD like booklet that I can use for more playtesting / subjucating my friends to my bad game design.