I'll be up-front about this: I hate Free For All (FFA) games, especially Slayer, so I don't really have much to say about them. If there are some high ping FFA players out there that are having luck with certain tactics, feel free to email me and I'll put them here. I tend to prefer team games, as well as games with non-slaying objectives like Oddball, King of the Hill, Race and Capture the Flag, so I'll comment here on how dealing with lag affects those games and your role in them.
Capture the Flag
You've got a choice when playing CTF as a high ping bastard: do you want to play effectively, or do you want to go for the glory and risk being hated by your teammates?
There's no question that players with high pings are better suited to defending than attacking; especially if you have a vehicle such as a Ghost or Warthog, or even a Shade turret, to help you. (Teammates, of course, are even better.) Grenades are your friend while defending, if you can work out with your fellow defenders where you're going to throw so they don't rush in for a melee kill as you're lobbing one. (Work this out in advance of the battle, in the lull between attacks, not just as you throw one, unless you're using some sort of voice commo-- which for the high pingers, is pretty much ruled out as it eats up your bandwidth).
If you die (which you may) in most CTF games you'll spawn relatively close to your own base, giving you another shot at the flag carrier before he makes a clean getaway.
If you assume that high ping players are going to die more often (and in my experience, they do) it's better to have them defending; they know what's going on back at the base, and they know which way the attackers went, so they know how to respond when they respawn. If an attacker dies and respawns back at the base, he's not of any immediate use there unless he knows the situation, and more likely he's just going to be focused on getting back on the attack.
As a high latency player, if you're involved in a coordinated attack you run the risk of upsetting the plan by dying early, driving poorly, or creating unintended friendly fire, and thereby drawing attention to your high ping in a negative way.
However, when you defend, if you're a high ping player all by yourself, you can always blame the lack of help and your high ping; players on the attack are unlikely to blame their defenders in these situations, mostly because they don't want to defend themselves. Note, better players don't behave like that-- they do well on defense as well as attack and know when each behavior is appropriate; however, there are plenty of players around who only want to get the glory of flag captures and care nothing about defense (not to mention those who play CTF games as if they were Slayer and care nothing about flags-- their own or anyone else's).
In short, if you're confident that you're contributing to a successful team effort even though you won't get many kills, may have quite a few deaths, and may not score a capture, then do it: good teammates will appreciate your sacrifice. And if they don't, you can always betray them and take the flag for the capture over the last couple of meters.
Team Oddball
High ping players... this if your game.
Why?
As the object is to rack up as much team time carrying oddballs as possible, and you can't use a weapon while carrying, all the issues about weapon selection, leading your targets, and compensating for lag while aiming all go out the window. Once you've got a ball, hide. If you can't hide, run. If you can't run away, get right up on your opponent and melee them with the ball; you might just get a kill. If your opponent is using a weapon with lots of splash damage, you might die but he might suicide in those close quarters, which in most cases means you'll be back in the game before he will, which is good news for you. This happens quite a lot in Team Oddball games in Prisoner with rockets, which is a popular gametype. And if you travel in loose groups, hopefully another teammate can pick up your ball. Getting too close isnt' good because you run the risk of having too many of your ball carriers taken out by grenades or rocket launchers.
Unlike flag games where a single object is the focus-- the flag or the player carrying it-- ball games allow high ping players to hide anonymously in their team. Most players aren't going to bother to cross-reference the player list to see which ball carrier has the highest ping and then look for him. If you get a ball, do the safe thing: find a dark corner somewhere and hang out for a bit. If the game has a motion tracker, stay still for awhile. Although, if the game has ball indicators, you may read like an "open" ball and draw attention that way, so be forewarned.
Some players may not feel this is a "fun" way to play-- grabbing a ball and then avoiding combat. All I can say is that I guess Team Oddball isn't the right game for you. However, it is one of the games that high latency players have an almost equal shot at, which is a plus in my book.
Ball carriers with panache can drop a ball, fire a weapon to take out an opponent, then pick up the ball again while losing a minimum number of seconds. My advice to lagged players is, don't try this. Just about any ordinary task that a player needs to do: entering/exiting vehicles, swapping weapons, etc., can be affected by lag. There are times when just switching the weapon in your hand for one on the floor can be an exercise in frustration; especially if you're in a hurry. You don't see the animation until a few moments after you hit the key, and if you wait to move until after that, you'll be dead during a firefight. However, move away too quickly, and you'll notice the switch never happens at all because you weren't positioned properly when you hit the key.
Add in the necessity of picking up the oddball-- which happens automatically-- and this can be a downright nightmare. You can find yourself dropping the ball to shoot, moving towards an opponent to fire, and then picking up the ball again as you advance, meaning that your next trigger press drops the ball again instead of firing. This is a good way to die. And backing away from the ball as you throw it is probably not any better; if your opponent has any wits, he'll grab the ball, turn and run before you can shoot.
Leave the flashy crap to the guys with cable modems: you just want to play a good solid game, which means trying to keep everything simple.
What if you aren't a ball carrier? Perhaps all the balls are taken? Try to play spoiler; attack opposing players and if you can to stop them from attacking your teammates, but avoid doing so with splash-prone weapons like grenades or rocket launchers. Killing everybody only helps the enemy.
If you haven't got a ball, don't bother hiding or camping. There's no incentive here; the number of times you die barely affects anything, as the score you receive for seconds of ball-carrying will just about completely override anything you could get by having a good kills to deaths ratio. If you've got a ball, run and hide; if not, rush in like a crazy person, as long as you aren't doing in your teammates as well.
Team King of the Hill
As in the oddball games, the playing field is evened a bit for lagged players in King of the Hill because there is slightly less emphasis on accuracy in combat and more placed on teamwork, planning, and tactical decisionmaking, especially in KOTH games on maps with vehicles. If you can coordinate a group to assemble, choose a vehicle, converge on the hill while eliminating nearby targets without getting mired in pointless combat, you can have a fair amount of success. Once on the hill, set up a barricade of vehicles and hide behind it. Allow enough space between yourself, the barricade, and the nearest wall to save yourself from splash damage or flying vehicles. Watch out for grenades; if needed, move off the hill and then back on after they've exploded.
Of course, because unlike oddball you can't just run away, combat is usually inevitable unless you've got a team full of low-latency sharpshooters or your opponents are just plain clueless. Your objective here isn't actually to rack up a number of kills, or even to survive: just to maximize time on the hill. Ideally, you want to go ahead and get killed-- just as the hill changes location. Chances are, on most maps you'll be just as close-- if not closer-- to the next hill location when you respawn than you would have been if you'd survived.
This also brings up another KOTH tactic that is worthwhile regardless of lag: don't always just rush off towards the hill no matter where it is. Learn where the various hill locations are. If you respawn far away from a hill and no vehicle is available, don't just set off on foot. Wait. The hill may be closer to you, maybe even right where you're standing, in just a few seconds, or a vehicle may respawn near you that you'd miss if you just ran off.
The same warnings apply to driving in KOTH games while lagged as do to CTF games; if you notice a lot of "warping" on your connection, definitely don't be a passenger, don't drive unless you feel fairly confident, and only man the gunner's position on regular Warthogs, not Rocket Hogs.
As in the Team Oddball game, if you're nowhere near the hill and don't have a vehicle, just try to prepare yourself. Gather weapons and grenades. If you have an opportunity to engage an enemy, consider his armament and yours before doing so. If you've got a long-range weapon, try to take out enemies who may be advancing on the hill. If not, consider doing nothing but wait-- if you fire on an opponent while you're outgunned, you're only drawing attention to yourself, and all things being equal you're at a disadvantage compared to a player with a faster connection. Wait for the next hill change and see what the situation is then.