As anotherdave said, don't say it unless it needs to be said. If someone has asked for your opinion then beginning with "In my opinion" is redundant (but better than saying "uhmm" or "errr").
For those times when it is appropriate then I suggest:
"It seems to me that..."
This takes a little longer to say than "I think that" or "I reckon that" so give a little more thinking time. "It seems to me" comes across as far more matter-of-fact but really means the same thing - just with more confidence. It seems to put the onus of truth on the statement (on the thing making you think that) rather than yourself. If it turns out that you are wrong you can blame how it seemed rather than your opinion.
"It occurs to me that..." is even more matter-of-fact but still not completely. The listener would expect the following words to be true. However, you have a get-out clause if it turns out that they are not: you did say "to me".