I'll offer an alternate view. I made a 10 day stop in Iran (in February). I am also an American citizen. I went with two fellow Americans. We worked with a travel agency in Tehran, the visa took less than a month and the trip was generally flawless. We happened to be in the region and figured it was worth a shot.
The gov't is terrible. However, the cases mentioned above of 'spies' crossing over have been instances of people being where they shouldn't. Now, that is a tough line to draw since the borders aren't clear. Nonetheless, as far as I know, there has not been a case of tourists, going in with approved visas, having any sort of issues.
We also had a 'guide' who happened to be this 50-some year old man who had spent 4 years in America in the 60's. He loved America, didn't care where we wanted to go and what we wanted to do. As long as we got back at night by 1 am and called him to let him know, he was ok.
Again, the gov't is fucked up. The people are not. I have visited over 50 countries in my lifetime. I have never met a general population as pro-American as the Iranian people. Everything they want but cannot have is symbolized in their minds by America. While they generally do not like American foreign policy, they love the idea of America and what it offers to its people - most of all, the freedom to live day-to-day life the way one wants to. Finally, the history is incredible.
I am pretty sure there is a British embassy in Tehran, we walked past it multiple times a day. Iran is quite cheap. It is not a particularly poor country however but day-to-day expenses are quite reasonable, especially if you don't have to incur the cost of a guide. There are also quite a few tourists in the country, something I did not expect. Mostly Aussies, Kiwis and the French. Obviously lots of bus loads of Koreans and Chinese too but that is to be expected.
Where are you thinking of going? We flew into Tehran, spent a few days, then flew down to Shiraz. Over the next week, we drove all the way up to Tehran with stops along the way. The highlight of the trip was the hospitality of the people, followed by some of the historical sights. Walking through Persepolis made almost every ruin I have seen growing up seem like a waste of time. Isfahan is also a really pretty city and if the gov't wasn't psycho, would be filled with tourists in any other country.