1. Giving advice
You should…, You ought to…, Why don't you…?, If I were you, I would…
2. Expressing opinion & agreement
In my opinion…, I think that…, As far as I'm concerned… / I agree, That's right, I'm afraid I disagree.
3. Apologising and requesting
I'm terribly sorry for…, Please accept my apologies. / Could you please…?, Would you mind …ing?