I made it to the silver leagues when people started cannon rushing me in almost every game. I'm always protoss, sometimes terran, but never zerg. What is an effective way to get rid of those pesky enemy probes when they send three of you after you, all going in different directions? 1/3 times I can successfully defend my base, but I still don't like those odds. I have an easy time defending my base with terran, as lon as I have at least one marine, but when I'm protoss (almost all the time) I only get stupid zealots which are slower than probes.

I've never had an issue dealing with one as Terran. If they try to be aggressive with the first cannon, I pull workers. If they try to slow push I have marines up and just kill the forward cannon, I've never not been able to find an angle to hit it. Once you get a Marauder it's pretty much done with.

What I've seen in PvP is just sending a zealot to the opponent's mineral line. If it gets there you essentially auto-win.

Advice for protoss: If they send more than one probe, do not try to kill them all. This is a massive handicap to their economy early game, and you need to take full advantage of it. If you build your own cannons in your base, it becomes impossible for the rush to advance. As long as you build less cannons than them and you keep your worker production on track, you have the economic advantage. As soon as your opponent's progress is halted, quickly tech to immortals and proceed to roll your opponent. In silver league, people probably won't have the sense to change strategies once you shut down the rush, so you'll probably either have to fight through a contain or use a warp prism. Do whatever you can to get military units in their base as quickly as possible after you stop their cannons; odds are that they have nothing there. If, in the event that they stop building cannons in your base once they see your cannons, don't try to rush them, as they'll probably have cannons, or an army, in their base by the time you're ready to attack. Instead, expand (probably not to your natural, as that's pretty close to all of those cannons). They definitely won't have the minerals to lay the hurt on you any time soon, so start bulking up.

Alternatively, for more lulz, consider an early expand to their natural and try to get a gateway there as soon as possible. Once you have a zealot or two there, march in and win.

Also, watch these videos if you really want relevant advice for improving your game. Videos 1 and 2 are probably the best for you, but Day9 is a great source for all things melee.

Yeah, but people learn to send in three probes at once, all going different directions. I normally take out 2 probes before cannons start hitting my probes. When I go for the cannons, they just build more. I try getting the pylons, but the he builds more around the same spot. I don't know what to do. Go after cannons, pylons, or probes? I talking about PvP of course, not TvP since I have no problem with terran. Thanks for the videos. Audio and Video are off on the videos, and it hurts my brain...

If the videos there aren't working, they're also on YouTube.

Again, if they send more than one probe, don't worry about getting rid of it. This is an all-in strategy that's easily countered if you remain calm and just avoid their cannons. If they start trying to put cannons somewhere new, just put down your own cannon within range of the new pylon, but out of range of the existing cannons, and they won't be able to push anymore.

Also, if you don't have a forge by the time the cannons start bearing down on you, but you do have a gateway, it may be better to just go straight to stalkers. They can snipe pylons if your opponent tries to build too far from their established lines, and, with proper micro, a small group can take out the whole rush.

I know that last part, on PvP, 1/3 of the time I successfully defend my base, but I don't like the odds. The guy in the video may be a dork, but he's helpful.

PVP. Don't make more than 1 zealot at start. Immediately tech to stalkers. Mkay?
However, if you scout and see double gate, do not tech to core. You will need to double gate yourself. You will be behind in zealot numbers. Unless you somehow manage to kill more zealots than you losing it, it won't be smart to go out of your base. You tech there after your entrance is somewhat safe, and then go out. That should not take over 7 minutes of your game.
Also, being aware of your opponent is very helpful in your games.

When did this stop being about fending off a cannon rush?

It didn't. You won't have trouble with a cannon rush with that build. Cannon rushes are quite stupid you know.

Well you could go fast expo, don't build your gas and fend it off from there...
Another move would to be rush into there base with your workers and as many marines/zealots as possible