Like you I also mostly use 0.05 and 0.03. Thinner the better, and brand is Uchida Yoco Made in Japan. For years I was Micron but then I discovered Uchida. Pen is about 1.5€ here in Croatia, and it can last longer then Micron. Love those pen. Even address looks fantastic… You can check It on my IG: vuky91
Cheers, Hrvoje 
I haven’t bought any pens specifically for writing postcards yet. I tend to use whatever pens that I have laying around. I’ve got a stock of different ones from places that I have visited.
I like using different colours though.
There is no better pen for a postcard than a Sharpie. Dries almost instantly, comes in lots of colors, won’t bleed even if soaked in water. If I am sending in an envelope I may use a fountain pen, “fun” pens, or whatever. But for a postcard sent “naked,” I turn to my Sharpies. Now that I am in Germany I have tried several German equivalents but they just don’t compare. It costs to have Sharpies shipped from the U.S. … but it is worth every penny IMHO.
I have just ordered a pack of 4. Looking forward to trying out a Sharpie for the first time of my life.
I use a Sharpie ultra fine point in whatever color matches the card. I usually get the set of 10 or 12 assorted colors, which includes red, dark blue, medium blue, green, orange, brown, purple… I never use the black or yellow pens on cards, because you can’t see the yellow and black is too mundane. 
I think that maybe, I’m a little bit crazy about pens. I have many penfriends, so I write quite a lot and send many postcards through Postcrossing too. I like to try pens so I could possibly find the best for me. I stopped a little bit to try, I did not do it for a while now.
My choice depends on the texture of the postcard surface and what I have to write, which style.
Among what I have, here are my favorite :
For brushlettering to write “Hello” or little quote at the end of the postcards:
Pilot Precise V5 RT
Black
0.5 Extra Fine
It’s the only pen that I use for both home and at work. When someone borrows it they always compliment as to how nice it is. If the writing surface of the postcard is somewhat matte or glossy, then it smudges easily and I have to let it dry. Otherwise it dries almost instantly.
I’m going to be buying some erasable pens. 
I do have a favourite I have used in the past that is erasable. I make minor mistakes when writing and I don’t want to use a twink or make it look messy.
Thanks for this great topic! I love all the wonderful suggestions I’m reading here. I am slightly obsessed with pens too, although I’m trying very hard to not accumulate too many of them. Until recently I’ve been on a search for the one perfect pen that would serve me in all circumstances and perform beautifully on all kinds of paper, but now I realize I’ve been on a fool’s errand: with the wide range of papers and even postcard surfaces, as well as the wide range in my moods, there will never be one perfect pen for me. But these are some of my current favorites for writing postcards:
Uniball Signo gel 0.38 mm in black, blue-black, and blue. I buy these refills for the Uniball Signo 207 and use them in Zebra Sarasa clip pen barrels, which I find more comfortable and attractive than the Uniball barrel. I use Uniball ink because it’s advertised as also being good for thwarting check fraud.
Sakura Pigma Micron 005 (0.2 mm) in black and blue. The ink is permanent and archival/acid-free. The blue is a turquoise blue that to me mimics (at least a bit) the shading of fountain pen inks. It works well with all but the glossiest postcards.
Sakura Microperm 01 (0.25 mm), black. This permanent, quick-drying ink is for the glossiest postcards where even the regular Pigma Microns won’t work. It’s also good for writing on plastic, photos, etc. It’s like the ultra-fine Sharpies, but with a finer line. Judging from some of the comments above, I think I’ll be trying out the UniPin next, because it seems similar to this Microperm.
Ohto Rays Flash Dry gel 0.5 mm in black. This ink writes smoothly and dries quickly, and I use it on postcard surfaces where I don’t mind a thicker line than what I normally prefer. I like the retro look of this barrel, and it feels very comfortable in my hand and improves my handwriting a bit.
Marvy Le Pen fine point in blue and Oriental blue. I just like the vividness of the colors, and for some reason these pens also feel comfortable in my hand and improve my handwriting a little.
I use whatever pen comes to hand.
I usually use ballpoint pens with black ink; any brand will do. I do have some colored ink ballpoints I bought at the Family Dollar that I’ve used recently for some postcards and greeting cards. I find for affordable writing and mailing supplies (envelopes, tape, etc), dollar stores have good items
Two other types of pen I use in my post cards are Pilot Precise V5 and Uniball.
I’ve heard a lot about Marvy Le Pen and maybe one day I’ll try it!
For me, a ballpoint pen of the cheapest kind is always my favourite, but recently I have been having the problem of railroading (when the ball of the pen writes funny and the lines come out like two parallel lines, like a railroad track) so I recently bought a Sakura Micron PN. I have the regular ones but because I’m a really rough writer (I push down hard on my pens), I keep ruining the nibs. The PN model stands for “plastic nib” and the thickness is variable according to how you’re using it. I’m unsure if I like it more yet, but that’s what I have been writing my postcards with lately.
I know the problem with having a heavy hand. This is why I have destroyed a lot of pens. Therefore I like ballpoint pens or gel ink pens better. They are simply more sturdy.
I’ve been using my fountain pens lately!! On glossier cards I use a Sharpie ultra fine too…or my Pentel Energels/Parker pen with a gel refill. I’m afraid I’ve got other gel pens as well but I don’t reach for them that often anymore (Uniball Signo 0.7, MyGel 0.7).
Gosh this sounds like me! I used to kill similar pens to to the Sakura Pigma/Uni-Pin pens because I push down really hard. 
That sounds familiar.
A German made Rotring Tikky Graphic Liner 0.3!!! <3
Sharpie Ultra Fine Line pens. Nice dark lines and easy to write on most postcard surfaces- especially the ones that are shiny or laminated on the back. The don’t smudge either.
A fountain pen Kaweko brass sport Fine nib, sometimes a Twsbi eco. But the main question for me is how is the ink if the postcard takes rain for the recipient ?.
I received my pack of Sharpie Ultra Fine Point pens today and I’m totally disappointed. They don’t meet my demands in any kind. The ink isn’t deep enough, feathers and bleeds on normal paper. And the “Ultra Fine Point” is a joke. The line width is more like the one of the Sakura Pigma Micron 08 which is 0,5 mm. Sorry Sharpie lovers 
The picture shows the Sharpie compared to a real ultra fine point, the Sakura Pigma Micron 003 (0,15 mm line)
Thank you for the visual comparison. I was wondering how thin this pen was, too.
