He's Wrecking the Country
No he isn't, Tony Blair and Gordon Brown did a pretty thorough job of wrecking it before he even came to power.
At the height of the last economic boom, back before the Labour government, not surprisingly, started hiding the Public Sector Borrowing Requirement (PSBR), Labour were borrowing huge amounts of money.
The PSBR is, or was when it was still being published, the difference between the government's income and it's spending. In good economic times, the government didn't usually need to borrow money, in bad economic times it did.
Except under Labour. They were borrowing large sums in both good and bad times. It is therefore not surprising that when the global economy plunged into recession and government revenues dropped that the wheels came off.
The situation is similar to one where a person who is borrowing on credit in order to pay their monthly expenses suddenly loses their job. Labour wrecked the British economy, and it's still not definitely known how badly (at least two trillion pounds of debt). Think Greece.
David Cameron didn't wreck the place, he's trying to fix it. This doesn't mean he's doing a good job, or even going about it the right way, but Britain was pretty thoroughly wrecked by the previous administration before he came to power.
I can't see why he actually wanted the job, I would have been tempted to say, "Labour wrecked it, they can fix it," because even if what he's trying works, it's doubtful he will get any credit for it. It would serve Labour right if they had actually won the election, although at that point, emigration would probably have been a good idea for the rest of us.
It must certainly be tempting when being pressed in the House of Commons by Labour about why these cuts are being done to turn round and yell "Because you ******* idiots lost all our money!"
He was Never Elected Prime Minister
Yes he was. The Conservatives had the largest number of seats in the House of Commons, that means the leader of the Conservatives has the most right to be Prime Minister. He didn't have to form a coalition, he could have formed a minority government, a government type that is even rarer than coalitions because it is hard to pass any policies, but he was entitled to do it.
The only alternative would have been a Labour coalition, with a Prime Minister (Gordon Brown) who was most definitely never elected by the British public, having come to power after Blair resigned. He never won an election, and had less real right than Cameron.
A "Rainbow Coalition" (described as a coalition of losers by The Daily Telegraph ) was proposed by the leader of the Scottish National Party (SNP) and, if you think a coalition of two parties is bad, imagine what one composed of half a dozen parties (or more) would have been like, especially as any party in that coalition would have demanded a cabinet seat, even if they had no real right based on the number of seats won (for example, the Green Party).
This also totally ignored the fact that Plaid Cymru had no real interest in forming a coalition, preferring to vote for policies they actually agreed with, and that Scottish Labour and the SNP don't get on very well, probably because the SNP want an independent Scotland and Labour most definitely do not - they don't want to lose 50ish seats in the UK Parliament.
David Cameron was elected Prime Minister. Why he wanted the job and whether in the long term he will actually be a good one is another question.
He's Breaking his Election Promises
No he isn't (this applies to Nick Clegg too, and to an even greater extent).
Although he was elected Prime Minister, he didn't actually win the election, defined as getting a majority of the seats in the House of Commons, he just got the most seats. Election promises are those you make (and, admittedly, later break) before being elected about what you will do when you will the election. No-one won the election, so we are in the rather odd position where it is actually impossible for anyone to break an election promise.
A matter of semantics, to be true, but still accurate.
He's Wrecking the Armed Forces
True, but not his fault.
Cutting back on the money spent on the Armed Forces, laying off soldiers, sailors and airmen and not replacing equipment or buying new is not good considering that our military has been under constant strain for over a decade now. There's going to be a period of time when our Armed Forces simply can't cope if they are needed elsewhere, especially as we now only have one aircraft carrier still in service with the decommissioning of the Ark Royal.
The reason behind this is the Armed Forces cost a lot, and the money isn't there. Labour blew it all; Labour MP Liam Byrne left a note for his successor at the Treasury saying "Dear Chief Secretary, I'm sorry to tell you there is no money... kind regards and good luck." 
Whilst Cameron's actions with the Armed Forces are appalling, blame the true culprits behind this.
Hate Them for the Right Reasons
Politicians provide so many genuine reasons to be hated and mistrusted - lying, thinking we're idiots, fiddling their expenses, letting foreign countries extradite British citizens without a fight, being politicians - that there is no need to make stuff up as an excuse. Someone who studied Politics as a degree is somewhat untrustworthy in my opinion anyway unless they're going into teaching or commenting.
And, before you ask, no I did not vote for David Cameron or the Conservative party. I just think it's unfair for people to be wrongly blamed for something that isn't their fault. Even if they are a politician.