I played a lot against IP today, and though I think I could've done better if I weren't sick, losing all but two of about 15 games is still pretty sad. I'm the P (or T, some games), he's the Z.

Problems:
After initial scouting, I can't see what he does until I get to observers.
Going light on army to tech leaves me very vulnerable to him waltzing in with his zerglings.
He can fend off any rushes or early attacks with the two colonies.

I tried several strategies against him that I've never tried before. I went early phoenixes twice. It worked the first time and I won, but by the second time he was well-defended enough to still out-army me.
When I went early DTs, he once zergling'd me and the other time scouted the tech.
When I went for zealot rushes, he was able to fight them off by having a colony among his workers, having his queen, and having the ability to create ten zerglings at once. Pretty pointless.
Whatever I went, he used mutas to harass my economy, forcing me to spend thousands on defending it with cannons (first time I've seen his use mutas ).
Basically, I can't scout him until I have observers to see specifically what he's massing, but going tech to observers may leave me already screwed over because it limits my anti-air capabilities. He can create larger armies than me when needed (being on the offensive, he generally has more resources, and Z in general is just better at macro possibilities), and my only real counter to the numerical disadvantage, colossi, is targeted by mutas and die very easily.

It's just... egh. I think I can do better than that, but since IP got to make a thread asking for help, here's my turn. I need epic ways to counter him. And, yes, I know how to play P, I know the typical counters, etc.

Psi storm vs. mutas
Colossi vs massed ground, specifically hydras and roaches - try to get a high ground advantage, don't forget the thermal lances, etc.
make sure to get plenty of sentries early game to block your ramp from zergling harass.
A few cannons can help against mutalisks.
Stalkers are your friends. Early-mid game, a good army composition has mostly sentries, stalkers and zealots - it's decent against most stuff zerg can throw at it except mass hydras, which he won't be getting until tier 2 now. Roaches die fast to immortals, and you should always throw down a robo for observers anyway. If you can't/don't get immortals, stalkers are the next best thing vs. roaches. Transition to robo quickly is generally a good idea.
If you find yourself untouched early on, grab a starport and harass him with a void ray or two. Killing his queen shuts down major army production until he can get a new one.
Map control is essential, as always. If he sneaks an expansion somewhere, it'll bite you in the hind end quickly, because his income will far exceed yours and zerg can always spend on something.
Versus banelings, your best option is to force field up - so get sentries. Lots of 'em.
Always keep an eye out for nydus worms. Don't restrict yourself to fighting fair - dirty tricks win games, so backdoor him with warp prisms. Get a few phoenixes and DTs, snipe overseers he brings along, and half his army dies to invisible blades that he can't do a bloody thing about.
Heck, get phoenixes anyway - sniping overlords will slow down production, and if you can grab a queen kill or two so much the better. If a phoenix kills two overlords, it's payed for itself in time and money.

I'll write about TvZ later. Mostly siege tanks.

Archons are the bomb when it comes to obliterating Zerg armies.

Abuse sentries, colossi, stalkers and high templars.

An interesting thing to note is that corruptors do have energy, but their abilities are seldom used. Even so, feedback outranges their ability, so high templars can be used as an anti-air for your colossi. High templars are also good for killing annoying infestors.
Guardian shield and force field are extremely useful against Zerg players.
Colossi, once upgraded with range boost, can snipe just about anything, and roast armies.
Stalkers... well if you've ever blinked into a defeated army just to kill off stragglers, you know the opponent's going to be mad.

Well, a lot of how to win in PvZ is in the opener. Here are two that I've been able to use to beat my friend, who is a better player than I am.

10/10 Pylon Gate in to forge, FE and then a relatively late stalker. This works great because you get to put early zealot pressure on and often force them to abandon an attempt at a nat. Your first timing comes when you get stalkers and can beat the roaches or lings they may have made to deal with your zealots. This pushes a zerg in to a defensive position and forces them to waste drones/larvae on defenses and lets you defend against any attacks with cannons/zealot to choke. After that, you can usually figure out something to do to reply. Since you have cannons, you can safely tech to Robotics while making one cannon in both mineral lines. Since you FEd, you can afford to do so and it protects against harassment, which is a common response from a zerg who is behind in macro. This is my favorite way to do a straight up Colossus play, because it lets you keep advantage until they go hydralisks.

Another solution is to go for fast stalker, but to suspend probe production at 15 in order to get a second gateway between the first gateway and the cybernetics core. If you play it right, as soon as the core finishes you can chrono boost two stalkers simultaneously and attack. This lets you get there with stalkers before most players make spine crawlers, and if you build two more, you can often do a 4-stalker push and snipe a queen or an FE or some zerglings before speed.