Exchanges handle probably thousands, if not more, of transactions a day. The addresses you've been watching could be exchanges sending their customers the withdrawals they've requested. Or maybe it's a mining pool's address. A large no. of transactions does not make a certain address "dodgy".
Exactly! Exchanges was the first thought I had. An individual won't be making thousands, not even up to hundreds of transactions per day. But on exchanges, every single minute, there's a trade, and a trade simply means the movement of funds.
always found it strange 
It is actually no cause for worry 