I use a backpack.

-Running errands I just hop off the bike and take it with me. Easy that way.
-3 Liter hydration bladder that works great for my longer commute on mondays, plus any cruises out in the country side.
-Pretty good wicking system on the pack along with a wicking shirt mean that there is little sweat kept on my back and what is dries quickly when I take off the bag.
-It doubles as a spare backpack for anyone who needs it when going backpacking.
-Holds everything I want- including groceries when needed.

Plus with the compression system on my bag, combined with the suspension system problems such as sore armpits and similar awakard things are not an issue.