Assuming you mean a felt-tip marker with a flexible nib—rather than a traditional India ink reservoir lettering pen wide metal nib—this may or may not fill the bill...

http://www.utrechtart.com/Faber-Castell-PITT-Artist-Pen--Brush-Sizes--Da...

…available in a wide range of colors.

Maybe Copic markers are what you are looking for:
http://store.copicmarker.com/pages/overview-wide-markers

Sign makers use pieces of a kind of felt that they cut to measure to use for making broad strokes.

Yes, a felt tip marker. This does look pretty close. Id be using it to--what else--create brush script fonts. The only other thing that would be nice is if it was refillable with an ink cartridge, like these:

http://www.dickblick.com/products/pilot-parallel-pens/

(though these are NOT brush pens)

Bert, no not really looking for calligraphic style markers. If you have never seen a brush pen their tips look and behave pretty much exactly like a pointed tip brush would, though they are made of one piece of material, not a bunch of fibers glued together.

Its kind of hard to tell from the picture but the tip is not as hard as a regular marker, it is very flexible, and the width of the stroke is not changed by rotating the pen in your hand to a certain angle, as with a calligraphy pen, but by how hard you apply downward pressure. They are really quite fun to mess around with. You can go very lightly and have an extremely fine, whispy line, or you can press down hard and get a very thick line.

Yep, there’s one of these here in front of me. And a refill : )

A remember an exercise we did in art school: roll up a piece of fabric, flattish or spiral like. Secure with piece of string, dip in ink or paint and go for it. Adjust its behaviour by cutting with scissors, etc. In other words: build your own equipment. (We used reeds, sponges, carrots, wood splinters, household stuff, hand and feet…)

Ok, so where did you get the one in front of you?

as a cartoonist I looked for these for a long time, for doing sketches while on the go, where a brush and ink weren't practical. The best I've found is the Pentel pocket brush pen, a japanese version you can get online. It's refillable with a black cartridge:
http://www.pentel.com/store/pentel-pocket-brush-pen
you can also find it cheaper here:
http://www.jetpens.com/Pentel-Pocket-Brush-Pen-for-Calligraphy/pd/1793

Jason C

Jason, did you ever come across any that had exceptionally bold/long tips? I'm seriously looking for one that could create a 1 inch diameter stroke when pressed all the way down.

Also, one of the customer's review of pocket brush pen is worth posting here:
"Don't hesitate, just buy this pen! Feels like a real brush and restores manhood."

Ryan: I've never seen anything that could come close to a 1" thick stroke weight, if that's what you mean. That'd be more like sign painting than anything else. The pentel has great flexibility and sensitivity, but it's still only 1/8" or so thick and a half inch long.

Jason C

Seems like pentel does make a bold tip variety. Don't know how I feel about those bristles though.

I bought my Pentel Brush in art supplies store in Amsterdam (around the corner from my place there). I have seen it online, where I have also seen other Japanese brushmarkers, eg with larger brushes:
http://www.stationeryart.com/zebra-zebra-fd501-chinese-kanji-calligraphy...
http://www.stationeryart.com/pentel-pentel-japan-chinese-kanji-fude-refi...