It's that time of year when climbers who really need a firm date should strongly consider getting a reservation for the primary climbing highcamps.
MAY: Generally speaking, reservations for the climbing highcamps are not needed for the primary climbing routes (and that includes Memorial Day weekend.)
HOWEVER, if you want to climb Libery Ridge in May, consider a reservation if your trip involves one of the last 3 weekends (esp. Memorial Day weekend.) Reservations are recommended for any trip that includes a Friday and/or Saturday night stay in the following zones: Lower Curtis Ridge, Carbon Glacier, Thumb Rock. The spaces in these zones are limited, and the demand "could" be large.
JUNE: If you'd like to climb in June, consider a reservation at Camp Muir, Camp Schurman, Camp Hazard and along the Liberty Ridge corridor for trips that include a Friday or Saturday night stay. For the most part, there is little "reservation" demand for mid week trips, or highcamps on other climbing routes.
JULY: If you're climbing in the main "Corridors:" Muir, Kautz, Fuhrer, Schurman and Tahoma Glacier; get a reservation for any trip that includes a Thursday, Friday, or Saturday night stay. July is a very popular month to attempt the summit.
AUGUST: Generally speaking, demand for permits in August is similar to July. That is: SEE JULY! It's true though, the last weekend in August is generally slow everywhere on the mountain (i.e. don't get a reservation.)
SEPTEMBER: The climbing along the main corridors is usually quite good during this month, but it's generally very quiet on most of the mountain (even Camp Muir.) September can be an awesome month to attempt Mount Rainier.
Reservations are now being "accepted" by mail, but they will not be PROCESSED till April 1. All reservations mailed in before then will randomly selected on that date.
As a side note, getting a permit to climb Mount Rainier is much different than getting a permit to backpack around Mount Rainier. If you intend to backpack in the park, and particularly along the Wonderland Trail, get a reservation!