Mechanical, lore... I never have played them, just out of curiosity. Dwarves, goblins, halflings, gnomes etc.

Bit slower than other players (by 5ft a turn) but not much else that I've felt aside from that.

Technically dwarves are medium though, even with the reduced walking speed. 

Can't use heavy weapons...but eh. That's deal-able. 

Not really, no.  If a player doesn't go out of their way to play up the 'Small' in small characters, there's so little mechanical difference between Medium and Small that it's very difficult to tell there is a difference.  There's a few edge cases, but that's honestly one of the misfires of 5e.  The game does an extremely poor job of representing size and scale within its mechanical systems, instead relying on pricy oversized miniatures or a DM homebrewing stuff to make even the largest of creatures feel any much bigger than a regular dood.

Not really. I played a halfling gloomstalker ranger in a short campaign a while back. No noticeable difference. Just a great quote... "My world is just a forest of @sses."

Honestly, I can only think of a few instances where it even plays a role in the game:

1. It means that you struggle with heavy weapons. I've rarely been interested in them in the first place, so I doubt that this will be an issue.
2. You can squeeze through small gaps. This helped once on a campaign - our Hobbit, sorry, Halfling, was able to get into a fortress through an arrow slit so he could raise the portcullis. This is the one time that I've noticed a noticeable effect of the quality.
3. You can pass through the space of a larger creature. That's never come up, so far.
4. From what I've seen, they get a -5ft penalty to speed. In most battles, I don't hit the max movement, so meh. I've had a couple of battles where it might have mattered (one where we were spotted from afar and had to sprint to the enemy to engage them while they were loosing arrows at us, another where we had to beat a hasty retreat), but unless it's a really long distance (180ft+) or the numbers just work out that you lose a turn because of it, it's a meaningless drawback.

Outside of battle, it doesn't get factored into anything. So, I don't see such a minor reduction as meaningful. I've only seen an actual effect once.

Role-playing, yes. I ushered a female character past me at the start of the campaign, accidentally feeling her arse. They're a couple, now. When she goes to nudge me with her elbow it risks concussing me :D

I suppose, but it's not a hinderance.  It's usually for comic relief, interacting with an environment built for humans (assuming, obviously, that you're not a party of halflings visiting a city of gnomes).

Definitely not as much as it used to. Some of the small races have some racial ability or other that arguably traces back to their size, but the rules that say "if you're Small, then this and that apply" are far and few between. Racial penalties to stats are gone (good), racial bonuses to stats are going (not so good, IMO). It's a diminishing effect unless you play into it (which I'd encourage). 

I have with certain characters, specifically a halfling paladin with no good ranged attack options.  Had one encounter where she spent most of it trying to get into melee range.  (Thanks to an over-eager companion, initiative was rolled when they were all quite a distance away).  Even using the dash action, it took forever for her to close, and most (all?? it's been a while) of the combat was done by the time she got there.

Besides the heavy weapon trait and 25 ft movement speed which I think have been mentioned, the only other mechanical differences I can think of are certain racial feats that the OG stout races have. Otherwise, I DM a group that runs two dwarves and a gnome and they lean into it to varying degrees. Gold, alcohol, and beard management are common themes for the dwarves, and the forest gnome is kind of frivolous, family oriented, animal loving, and adventurous, though I think this is just who she is.

I played a game where I had a very tall character (almost 7 feet) and a very short character (2.5 feet) and the party had fun with it. Tall character could reach things no one else in the party could, and had to boost shorty over things every now and then. Shorty got captured and escaped because they didn't have manacles small enough and because he could squeeze into some places the others could not.

I played a halfling forge cleric for a year with a personality type akin to a small dog that thinks it's a big dog. I had a lot of fun playing her. I played up the height difference and the DM accommodated it by weaving it into the narrative. Mechanically though, there was no real meaningful gap. The speed difference is barely noticeable and as a cleric, monsters were coming to me just as much as I was going to them. The halfling wizard in the same party would climb up on the shoulders of the goliath warrior and fire off spells like a RR/Groot team up. 

During Curse of Strahd we were fleeing down Druid Hill and my Human Cleric was carrying the Gnome Wizard under his arm backward so the wizard could continue shooting. Lots of laughs there.

Same game but I was playing a Dwarf and we had a Halfling Monk of the Sun Soul who could essentially shoot sunlight from his hands. We had a lantern that would detect traps but I needed my hands free to hold my great ax. I set the Monk on my shoulders, handed him the lantern and told him to hold on. More laughs.

My current character is a Goblin-sized Warforged Artificer Steel Defender. He rides around on his mechanical dog Harley so the -5 Movement isn't a factor.

I play a halfling paladin, and it’s pretty sweet being able to use my mount in dungeons, since the  mount is medium, it can be in the areas that would be a problem for a horse. It really helps make up for my otherwise slow movement.
And once or twice I’ve used that ability that lets me (unmounted) move through an enemy’s square. Doesn’t come up often, but it’s really handy when it does.

Then if I need something from a top shelf, I get the Dragonborn to reach it for me.

My Halflings reject the term "Halfling" as it implies being half of something, which in turn implies being less. It's very insulting.

I call medium size humanoids "big 'uns" or "wee giants". Or "big stupids".

Our party of small sizes (Gnome, Halfling, Kobold) were members of the Diminunati, a secret order dedicated to promoting the welfare of the small folk.

Quote from terrywilcox >>

My Halflings reject the term "Halfling" as it implies being half of something, which in turn implies being less. It's very insulting.

I call medium size humanoids "big 'uns" or "wee giants". Or "big stupids".

Our party of small sizes (Gnome, Halfling, Kobold) were members of the Diminunati, a secret order dedicated to promoting the welfare of the small folk.

 

 I would SO play in this game! I can see a whole party of small folk and then you have that ONE guy who is a Goliath. The RP opportunities alone would be worth it!

Being able to use medium mounts isn't usually an advantage, but it does allow a battle smith artificer to ride their construct.