Loving the Random Encounter suggestions.  I had a feeling others might well have additions - fact being often stranger than fiction.

Mine were just from that day, but if we're "allowed" to go back in time:

4/1 The PC is on a world that speaks little Galanglic in a large transit nexus and have got into what they think is the right queue for their next tickets/vehicle/ship.  A sophont matching the character's age and gender taps them on the shoulder and says "not this queue, you need to be over here".  As they walk to the correct queue, the figure introduces himself as "Christian" <insert name appropriate to followers of whatever religion might be relevant> and shows an interest in the PC.  Getting to the right queue (as it will turn out) the PC turns around to find that Christian has disappeared (presumably) into the crowds [1].

4/2 The PCs are in a run down part of a city/starport/orbital station when they're accosted by a man in a trenchcoat.  He opens his coat to display a bunch of holographic images arranged on the inner lining showing sophonts in varying degrees of undress.  "I can find you friend," he says.  "Not cost much." [2]

4/3 The PCs are in a port that doesn't see much traffic.  There are several messages from the SPA saying that various locals are offering day trips for 1-3 people to show visitors the local sites and provide a good meal.  The outings are quite genuine and any characters who take up such an offer may well see some interesting sights - perhaps a local cave system and the interesting larva/worm/glowing insects that inhabit the caves [3].  There is a 50% chance the characters will be proselytized by enthusiastic members of an appropriate faith at some point(s) during the day.

4/4 The PCs are taking a tour to enliven a particularly dull port stopover.  The tour guide happens to know one of the characters' homeworlds as they ask where the group are from and has a painting/sculpture/hologram displaying some historical figure from that homeworld.  The guide is really chuffed to have such a personage on the tour and despite the clear signs and regulations saying it's prohibited, allows photography on the tour as an 'exception'. [4]

4/5 On a reaccreditation of a licenced skill in one port, a PC encounters another sophont on the course who is stunningly attractive and has the cutest accent.  (For whatever value of 'attractive' and 'cute' for that character).  The course takes a day in which the examinees get to know each other a little, and the trainers mention at lunchtime that there's a special recital going on that evening at a venue of historical interest that otherwise has a three month waiting list for visitors.  The PC may express an interest in time/place etc and finds, as it happens, the attractive fellow examinee is the only other person interested. [5]

4/6 On a backwater world, The PCs are delivering a lecture/briefing/illustrated-talk-of-their-travels to the locals who are desperate for any training/entertainment that they can persuade visitors to deliver.  One of the attendees shares a mutual interest/background/homeworld with one of the PCs and is an easy in for a trade/romantic relationship.

Hmmm, better stop now before I've regurgitated half my life history...

tc

[1] Yes, this I would claim as an encounter with an angel.  :-)  I was a young man a long way from home in time and space - two years I'd been travelling and I was down on the River Plate in Uruguay and alone for the first time in a couple of years trying to cross to a flight from Buenos Aires after a 24 hour coach trip with about six words of Spanish and a huge crowded transit hall between buses/coaches/ferries/fastcat etc.  I was following the other coach passengers - I'd been with assuming they knew what they were doing when the above encounter took place.  We only exchanged a few words and having just lived in a community that included 40 Germans and one guy called Christian, I didn't bat an eyelid at this guy.  But nearly as soon as I'd met him, he'd gone and I never found out more.  I was indeed in the wrong queue, he'd put me in the right one, and to this day I have no idea how he knew what I needed or any rational explanation for the whole incident.

[2]  Bangkok.  My one encounter with a pimp.

[3] This is how I saw the fascinating Waitomo Caves near Auckland in New Zealand with a short boat ride into complete darkness to see these critters that live up on the roof.  They sleep for a few months, "fish" (for small bugs) for a few days, procreate for a few hours (glowing on the roof) and then die as they have no mouths to feed at that point.  What a life!

[4] This is a short form of a much longer and vaguely amusing story I won't bore you with.

[5] Ahhh!  Marik!  And the Villa Tugendhat in Brno, Czech Republic.