How can I tell which Google Chrome channel I'm running?

Try chrome://version/

Regular Chrome says:

Google Chrome   14.0.835.186 (Official Build 101821) m
OS  Windows
WebKit  535.1 (branches/chromium/835@94713)
JavaScript  V8 3.4.14.21
Flash   10,3,183,10
User Agent  Mozilla/5.0 (Windows NT 5.1) AppleWebKit/535.1 (KHTML, like Gecko) Chrome/14.0.835.186 Safari/535.1
Command Line    "C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome\Application\chrome.exe" --flag-switches-begin --enable-print-preview --flag-switches-end
Executable Path C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome\Application\chrome.exe
Profile Path    C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome\User Data\Default

Chrome Beta says:

Google Chrome   14.0.835.186 (Official Build 101821) beta-m
OS  Windows
WebKit  535.1 (branches/chromium/835@94713)
JavaScript  V8 3.4.14.21
Flash   10,3,183,10
User Agent  Mozilla/5.0 (Windows NT 5.1) AppleWebKit/535.1 (KHTML, like Gecko) Chrome/14.0.835.186 Safari/535.1
Command Line    "C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome\Application\chrome.exe" --flag-switches-begin --enable-print-preview --flag-switches-end
Executable Path C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome\Application\chrome.exe
Profile Path    C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome\User Data\Default

Dev says:

Google Chrome   14.0.835.186 (Official Build 101821) dev-m
OS  Windows
WebKit  535.1 (branches/chromium/835@94713)
JavaScript  V8 3.4.14.21
Flash   10,3,183,10
User Agent  Mozilla/5.0 (Windows NT 5.1) AppleWebKit/535.1 (KHTML, like Gecko) Chrome/14.0.835.186 Safari/535.1
Command Line    "C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome\Application\chrome.exe" --flag-switches-begin --enable-print-preview --flag-switches-end
Executable Path C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome\Application\chrome.exe
Profile Path    C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome\User Data\Default

Canary says:

Google Chrome   16.0.891.0 (Official Build 102650) canary
OS  Windows
WebKit  535.5 (@95897)
JavaScript  V8 3.6.4
Flash   11,0,1,148
User Agent  Mozilla/5.0 (Windows NT 5.1) AppleWebKit/535.5 (KHTML, like Gecko) Chrome/16.0.891.0 Safari/535.5
Command Line    "C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome SxS\Application\chrome.exe" --flag-switches-begin --enable-print-preview --flag-switches-end
Executable Path C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome SxS\Application\chrome.exe
Profile Path    C:\Documents and Settings\geek\Local Settings\Application Data\Google\Chrome SxS\User Data\Default

Regular is m, Dev is dev-m and canary is canary

According to the official Chrome Release blog, your version is the latest stable version. I think if the version doesn't state either beta or dev, it's using the stable channel.

A little googling gives the following explanation of m flag.

// Return a human readable modifier for the version string, e.g. 
// the channel (dev, beta, stable). Returns true if this operation 
succeeded, 
// on success, channel contains one of "", "unknown", "dev" or 
"beta" (unless 
// it is a multi-install product, in which case it will return "m", 
// "unknown-m", "dev-m", or "beta-m"). 
static bool GetChromeChannel(bool system_install, std::wstring* 
channel); 

Source

The "m" just means that you have multiple versions of Chrome installed in C:\Users\username\AppData\Local\Google\Chrome\Application. You might have multiple versions of Chrome if you didn't download the latest version, but updated to it. The new version won't replace the old one, in case of installation failures. So in essence, when Chrome detects that you have more than one version of Chrome, it displays "m" after the version number in the [About Google Chrome] window.

Source (in comments)

It appears as if you are on stable channel.

You can just check the About Google Chrome as you already have and look for "beta" and "dev" version keywords. I'm running the latest beta channel version (on Windows 7) and my "About Google Chrome" window says "beta-m". An image of something similar to what you should see can be seen at How-To Geek