How does Syphir "delay" an email? That's simple: when the email arrives, Syphir automatically marks it as "read" and then marks it "unread" at the desired time. At first, I couldn't figure out why anyone would want to do that, but I've started using it myself with Google Calendar agendas. I have a Google Calendar configured to send me a daily agenda of events. In this case, the calendar is telling me about birthdays and anniversaries. The problem is that the email arrives around 5 o'clock in the morning, but I'm not actually going to do anything with the email until after 5 pm. Using Syphir, I can "delay" the email until the afternoon, at which point I get a "new mail" notification and can use the information much more readily.
You could also use Syphir to make it appear that you don't have any unread email between, say, 9pm and 9am (for those of you who wake up in the middle of the night and can't get back to sleep if you have unread email).
Syphir can also act on email that has been sitting around for a while. For example, if I'm reading my email on my Mac, I tend to archive it right away. If I'm reading it via the Mail app on my iPad, I tend to leave it in the inbox, even after I've read it, because it's more of a hassle to move it. I set up a Syphir Rule that says, "If a message is in my inbox for more than three days, and I've read it, archive it and label it auto-archived."
Imagine if your job required that you reply to all of your email (for example, a tech support mailbox). Syphir will also let you set up a Rule that will be triggered "if a message has arrived [1 to 24] days ago, and I haven't replied to it." Using that Rule, you could apply a label to those messages, star them, or send a notification to your iPhone.
Here's the latest Syphir Rule gem: "If an email is sent to more than five people, don't put it in my Inbox, but instead attach a label to it." Instantly all of the "mass emails" that friends, family, and co-workers send are shuffled off. You can also set rules for "exactly [1-10] recipients," which would allow you to apply a rule that says something like, "If this email is sent only to one person (i.e. ME!), then...." That's something I've wanted from Gmail since day one.
When used with the SmartPush application, Syphir can alert your iOS device directly using push notifications. With SmartPush, I can get notifications when certain people email me (my wife!), without getting notifications when *everyone* emails me. Using the "Number of Recipients" condition, I can get notifications when someone emails me and only me; that means that I can skip notifications of Aunt Millie's latest batch of cat pictures that she's sent to everyone in her address book. I've set up a rule to push notify me when I get a new Google Voice SMS or Twitter Direct Message, instead of using conventional SMS notifications.
Syphir also utilizes something called a "Reply Probability," which means that it tries to determine the likelihood that a given message will need a reply. I haven't used that one myself, but it sounds interesting. Syphir has some example rules that show off some of these features and how you might use them.
As much as I love Syphir, there are a few issues. The biggest is that I can't find a way to edit a rule once it is created. You have to delete it and create a new one (See update below). Also, the downside to using OAuth is that I frequently find myself having to go to Gmail and log in there, which redirects me to Syphir. It's not a huge issue, but it's a frequent irritant.
Lastly, there's one issue that is easy to avoid (if you know how); by default, Syphir only works on messages that end up in your inbox. If you have Gmail filters in place that "Archive (skip inbox)," they won't match Syphir Rules unless you use the "Coverage" condition and tell it to look at all incoming messages. To me, this makes total sense; I use Gmail filters to do the heavy lifting of most messages, mailing lists, etc., and I use Syphir for the more precise filtering that Gmail doesn't allow. However, it can easily lead to confusion if you are wondering why your Syphir rules aren't matching.
UPDATE: I'm not sure why, but some rules seem to be able to be edited and others aren't. I've uploaded a screenshot of what some of my rules look like, and some of them simply don't show the "Edit" button.