I always take water with me on my trips but the longer I'm out, the more likely it is I'll need to fill up in a stream at some point.
I've drunk out of many streams but there's some things I've come to learn:
I try and avoid drinking from streams if it's obvious that the stream is running through a field/hill overrun with cattle etc. Look out for cow pats and various animal droppings. The more there is, the less I'd be inclined to drink from that stream.
Drinking from higher up a stream is a better bet, I'd say. I've seen the odd dead-animal in a stream and the higher up you are, the less chance there is there'll be a dead animal further up. I'm not saying they'll never die at the top but you probably get it already.
Good tip for you is to check your map and see where the stream has come from. If it's passed any buildings, you don't know what has contributed to that building.
I once came back from a trip and had to visit my GP because I had a bad dose of the runs. I figured I knew why and chances are it was because I drunk from a river, down-stream from a farm that had lots of sheep and cows. Chances are various junk had polluted the water. The thing is, I never did find another source of water that day and I was getting thirsty. Should have just waited till the next day.
You can also buy droplets or tablets to stick in your bottle that are supposed to rid of the nasties in your water. I've got some of the drops but I've never used it.
Check the colour of the water, when you've filled your container. If it looks like water, great. If it looks a little darker than usual, it might be because it's passed through some peat. Nothing wrong with that, tastes great. You'll probably see that some time. I have once poured out the contents of a bottle after filling it because it didn't look like normal water and it didn't look peaty either. That's the only time I've poured it away though. I can't say I remember it smelling of anything, either.
Anyway, enjoy your drink. I love the stuff. Don't be afraid of it