We went the week of 6/16 last year. The cruise the week before us had high 70's low 80's, our cruise was mostly in the high 50s and low 60's, so it can really be a crap shoot. I would gues you can expect 65 to 70 degree highs with lows in the 50's, but again there is no gaurantees.
Bring a rain proof light jacket if you have one. We ended up buying them for $20 a piece (which was a good price for the coat) at our first stop. It can rain almost everyday off and on (its a rainforrest) but then again it can be sunny the whole trip too. Alaska is a hard cruise to pack for. The ship was comfortable the whole time, so if you have a good coat and maybe a sweater or two just in case you should be fine. I brought shorts but never needed them.
We went in mid July 2005 and encountered high temps in the 70s on a couple of days, highs in the 50s a few days, a fair amount of wind, and sprinkles periodically. If you like to be out on the deck while the ship is moving, take a warm jacket; consider the ship is moving at 17 to 22 knots, which produces a 17 to 22 knot wind. Also factor in some natural wind combined with cool temps and it can be downright cold. Definitely pack a rain poncho; you may or may not use it.
All in all, Jim C. is right on the money when he calls it a crap shoot!
We bought $1 vinyl rain ponchos at a sporting goods store - they are small, lightweight and pack away easily. We only needed them the day we were in Glacier Bay - sprinkles and in the 40's.... We went in ealy September, so didn't even pack shorts, but brought clothes to layer - slacks, tees, lightweight button down shirts/blouses and sweaters. Good walking shoes are a must.
Layers... you want to be prepared to add and shed clothes as needed. The weather in the Pacific N.W. is fickle. You can have the comfortable temps as described above during some days and it can from time to time drop to the low 40's high 30's at night on extreme days. The waterproof and wind proof idea mentioned above is the best advice. Make sure it has a hood.
Sweaters, turtle neck shirts, coat, outer rain/wind breaker, comfortable but rugged shoes/boots, insulated if you have 'em. If not heavy socks. As the Boy Scouts say... "Be prepared". Especially if you have a balcony or are going to spend time on the decks. The wind and drizzle can make you very uncomfortable if you get damp/wey.
We did a 7 day round trip from Seattle last June 4th. The weather was great 70 to 80 during the day. The only cool day was in Tracy's Arm. My Uncle bought a nice jacket at our first port Ketchikan. It was a very nice jacket for less than $30.00 bucks. We felt the best deals were at Ketchikan also.
Have fun on your cruise.
Definitely bring a raincoat - Ketchican averages 300 rainy days out of the year. Layers of clothes is your best way to go. You may need shorts for Vancouver/Seattle and find it gets cooler as you go up the coast. On our cruise, at the first stop in Ketchican so many passengers were off the ship and into the first store to buy hats, gloves, sweatshirts and coats because they weren't prepared.
You can go on line and pull up the national weather forcast and look up the 10 day forcast for any city. We've done it on all our trips. The weather has always been a little bit nicer than forcasted. Of course you need to check it every day up until the last day because it does change.