Definitely a towel - that's my top tip for Legoland be it wet or dry weather.
We were there last weekend and it was torrential. We all had raincoats with rain ponchos over the top though and the rain didn't spoil our fun one bit, in fact it meant the queues were shorter than usual.
Towel is useful for sitting on if the benches etc are wet while you wait for the dcs to come off rides and also, as bruffin said for the water play area if it's sunny. Also useful for drying wet hair and faces etc be it from rain or water related rides.
Have a look on the website, choose the rides you most want to go on, get their before the park opens and go straight to the ride your dcs want to go on the most. For mine it was Atlantis and Lazer Raiders. Don't queue up for Viking Splash on the way in, its much quieter later in the day, as lots of people tend to go there first, because it's the first ride you come to.
If it's cold and/or wet, going on the Atlantis ride is a great way to warm up, we went on it four times one day. 
Food is extortionate and horrible so a picnic is advisable and if it rains you can eat it in the Duplo puppet theatre, which is opposite a stand selling hot drinks etc. If it's sunny, its nice to eat your picnic while watching the Pirates
stunt show. If you do want to eat there, you can get a child's meal for £1 with any adult meal at certain cafes after 3.00 pm.
If your dcs like fizzy drinks, which mine don't, it's apparently good value to buy one of their refillable drinks cups, which you can then have unlimited refills in all day.
There are shops and merchandise in every area of the park - so be prepared for plently of pester power. 