I suppose a lot depends on your market. If you've been looking for ages have you gotten a good feel of what things are selling for and how quickly?
12 months ago we offered on a house we loved and confidently went 8k under the 175 asking price, with some negotiating we settled on 170.
12 months of been messed around and lead on by the sellers they once again walked away from a planned purchase on the eve of exchange telling us we'd just have to wait. This caused us to walk away.
As the market now was much more competitive with far fewer house available we knew we couldn't mess around. Most houses sell within a week, with many going in four days or less (unless there's serious issues) as such we went in 183 on a 185 asking price (prices had also increased in that 12 months so we're actually getting less house than the original) even then we had to up to 184 to secure it.
As good as the advice on here is, it all depends on your local market and what you're comfortable with. Ignore agents they have their own agenda. If houses sell quickly you'll need to be competitive anything within 5% of asking to me says competitive offer within 2% says bloody keen!
We've bluntly told agents on some shocking properties that we wouldn't want to offend sellers with an offer at the level we feel the property warrants (20% under asking or more).
But I know some areas (London) etc are a different world from what I know up here in the midlands. Without knowing the house of the area I can't offer much more advice except what's said above. Take a breath, have a plan and above all decide what the property is worth to you.