How to achieve that nice, fat but irregular borders in Inkscape or gimp or Photoshop Elements?

Borders like found in games called Paladog, Dungeon Rampage (you can find it on FB games) and most flash games, even most casual games.

I found some tutorials on cartooning but they're showing a regular border but irregular gives best impression.

Irregular may not be a best word to describe it. It doesn't look flat and in most tuts it does. Or is it just matter of good geometry? I don't think cause it may be a flat figure and it looks great. There's that style in cartoons like dexter.

I read that it's better to create that style in vector graphics program but I don't have iluustrator. Yet. Only inkscape for today :(

I'd be gratefull for giving tips or links to good tutorials

Those games achieve the mixed outline widths by overlaying parts of objects on top of each other.

What you can do is in Inkscape you create your objects, and when you're done you duplicate all the parts, unify them and add a thicker stroke to this unified matte. Then when you overlay the original with the thick outline, you get the effect.

Just make sure you're well versed with Inkscape's functionality with objects, alignments and paths (boolean operations, converting objects and strokes to path, etc. etc.).

Ok, but have you any tutorials showing how to do it in that style?

you may notice that style also in cut the rope on even birds.

nobody? is it a secret knowledge? ^^

Hello. I don't know of any, but I Googled for "cartoon outline thickness" and the first result is a tutorial about it.

In Inkscape, you can also convert the stroke of an object to a path (CTRL+ALT+C) so it becomes a shape that you can alter etc. and play with the nodes and tangents to get the dynamic shape you want.