I haven't offered this one all too much thought yet. But here's the current thinking...
But basically, one or two people are "it". They have to catch up to any non-it player and catch/tag them. And so on.
    • Should the player who is tagged lose his\her speed?
    • Should the player who is tagged be frozen for 1-3 seconds or so before they can move again?
    • Should players be visible on some sort of a minimap\compass thingy?
    • Should you be able to push other players, including the one who's "it" away?
I really like the sound of the game mode.  The player who is tagged should lose there speed and have to build it back up again.  I think they should also be frozen for a second or so to stop them insta-tagging someone else. I think you should be able to push players but not the one whos it (this also goes for the second mode i mention below, tagged players shouldnt be able to push, but untagged can push... "save yourself *pushes dinius away from taggers while i get frozen and tagged*) . 
As for visible on the map i see a few game modes.
Firstly, I see a game mode where 1 or 2 players are It and they then hunt the others. On tagging a player, the first player no longer becomes it, and the second player becomes it.  However, what is the win criteria on this mode?  I don't think if its 1-3 vs many a way to find other players is needed. As there should be enough other players to find people (maybe make it so that < less than 5 enemies you get some way of knowing where they are?)
The second mode i see is a kind of "infestation" mode, 2 players start out it, and they have to tag every other playe.  When they tag another player that player becomes it but the first person doesnt become normal, they are still it. This way eventually one person will be left, last person is the winner. As this gets to a low player count, some identifying way to find hiding players would be needed so again, maybe < 5 people left display a way to find them.. Otherwise people might just hide rather than running / freestyling around. Maybe in this mode, the person who is tagging should also be slowed / frozen for a moment so that they cant just multi tag 10 people at the same time (for this i think a slow would be better than a freeze)
The second one sounds interesting, hadn't thought of that. But I guess there's not all that many places to hide in an open map made for this, so maybe no compass or such imo... If you just hide you're screwed when ppl with speed find you, which they will fairly quickly. So a great jumper could keep up his\her speed and continuously avoid the ones who are it until the player is left alone as non-it. At which point it would be exceedingly hard to stay 'free'.. And then when he's finally caught the "round" will be over and the player will be the winner, and maybe that player starts as "it" the next round. 
On another note though,at the first method, it could just be ranked\scored by how much\little time you have spent actually being "it".
But I think the second way you mentioned would be more fun.
Yeah the hiding thing becomes a problem when you add everyone elses maps. Hidden rooms and such could become a problem.  Maybe do what gmod hide and seek does. It adds a glowing trail to the people still free.
So many great ideas here! I've always wanted to have tag in warsow ^^ Would you tag players by using a melee weapon or just by bumping into them?
I think they should also be frozen for a second or so to stop them insta-tagging someone else.
by Piercy
I'd say stopping the players, or even just setting their speed to something like 50% of the taggers speed, and not allowing you to tag for 1s after becoming "it", would make for more a smooth and less frustrating experience. The infestation mode sounds great! I also like the glowing trail thing, but would prefer that being an anti-camper meassure, where you get glowing trails to people that stay under a certain speed for a certain amount of time?
On another note though,at the first method, it could just be ranked\scored by how much\little time you have spent actually being “it”.
by Dinius
Super Mario War has a pretty decent system for tag. There's set time for each individual player, that starts counting down when they are "it", when the limit is hit, they die, and the player with the most time left becomes "it". This would likely result in people having to sit around and wait for a few minutes before they can play again, thought. So, maybe a good idea would be to allow "dead" players to run around as ghosts, still being able to push the living players. idk, just an idea :)
Imo just running into people MIGHT be a tad easy (or not, need to test with people). So was mostly thinking to have it like.. Melee like you said pretty much. You click "shoot" like you would with a weapon, player model reaches out a hand and tries to "catch" the other player. If the direction and proximity matches so-so, then you successfully tag the other player. (Needs to be somewhat forgiving though)
And agree, anything that kills your speed entirely feels .. bad :P
As with all game-modes, we should be able to configure all the relevant settings. For example, let the tagged player not lose speed, or let them simply not attack for a little while.
Also, ranged attack (railgun) tag would be nice.
I've been playing tag in CPMA for a long, long time, where we just play instactf and switch teams in warmup mode, 4v1, shoot someone to tag them and make them switch teams. A dedicated game-mode for this would be nice, since you can create really cool variables, like instant team-switch, different weapons (maybe like a really high-speed projectile?), enable weapons with no splash damage for other players (so you can rocketjump and etc., assuming rocketjumps exist in this game).
Might allow some settings changes eventually, but first off I think it's better to focus on making one specific ruleset\gametype for the new gametypes work good.
Modding gametypes to your liking should ofc be an option, but I suppose a change of labels if many things are different, so people know what to expect when joining the server. I.e. "tag" would become "custom-tag" if major settings are changed, perhaps?
Also, having railgun kind of defeats the purpouse of this gametype, imo. Not much use in running away from someone that can instatag you from any distance..
Agree @ railgun stuff, you could just stand still and shoot people.. 
As far as modding goes, depends a lot really.. Imo better to have a well worked out gametype, than having 10 servers with 10 different variations.
High reload time means you have to use it only as a last resort, if someone is running directly at you at a high speed. Balance is an issue to discuss later, but I don't want every gametype to be 100% strafing, the way HuPo does. There have to be special features in each gametype for it to be appealing at all: it doesn't matter if I'm strafing from A to B in a standard run, strafing in circles in tag, strafing from A to B while avoiding other players in CTF, or strafing just for the sake of strafing in a freestyle mode. Each mode need something special to make it unique, if that's special abilities, weapons, or something entirely different.