I was visiting in London and was with a friend, a Member of Parliament, and he took me on a tour. He was a very liberal member of the Labour Party and as luck would have it, Margaret Thatcher was walking through the hallway. They stopped and said hello and he introduced me to her. We shook hands and she was quite gracious.
When Obama was running for President, I went to a local rally and shook his hand.
I was driving my car just behind the small motorcade of Ugandan President Yoweri Museveni. It suddenly stopped, and he got out to help someone push their car out of the road. Lots of nervous bodyguards pointing AKs in our direction.
Oh yeah, I went to the after-summit staff reception when Ronny was in Moscow and listened to him sputter nonsense before his wife hustled him off the stage. On the plus side, I got to meet Dave Brubeck at the same reception. Also shook hands with SecState George Schultz.
I twice missed meeting Jimmy Carter, once at the embassy in Cairo and once at the embassy in Bamako.
When I was in grad school, Queen Beatrix of the Netherlands came for a visit, and I went to see her arrive… I was across the street, so about 20-30 feet away.
My folks took me to see LBJ go by in a motorcade when I was a kid. I remember that they spotted him but I didn’t.
Just as I figured, there are tons of people more connected than I.
I will mention I forgot to include Gabon’s mellifluously-named President Omar Bongo, who I saw the same day as Thatcher, from about 100 feet away.
Does he have to have been Head of State at the time? I was probably within 35 feet of Obama back when his candidacy was still “LOL, this guy?” I shook hands with Al Gore who was Vice Head of State. Do I get partial credit for that?
Elbow to elbow with Ford, waiting in a lobby and had just removed my contact lenses so my vision was impaired. The person I was waiting for later informed me about it.
I was part of the perimeter security of Obama’s landing zone when he came into town and screwed up traffic for hours to get a 20 second soundbite on the news.
I was in Baghdad in a different uniform pulling security on the convoy route when GWB’s motorcade drove by on the way to getting a shoe thrown at him.
Later that tour Obama was due in for his first visit but plans changed due to weather and he never flew into our location.
I’ve shaken hands with Prime Minister Chrétien, and been within 5 feet of Prime Minister Trudeau. However, they weren’t heads of state, only heads of government.
American: Not in office – but about a half block away from Candidate Obama; exchanged pleasantries with Bill, Hillary and Chelsea for a couple of minutes during that same 2008 primary stage (my pic with the Big Dog is on one of my RL social net pages). Did a quick handshake with W once while he was still a governor.
Not American: Was three doors down the hall from the President of Dominica.
Northern Piper, your HoS is not even in the same country most of the time!
When I was 15 I got to meet the Prime Minister of New Zealand, Helen Clark. My group was touring the Parliament House and crossed paths with her; she even stopped and took a few questions. I got to ask her if she had an official residence; which she does, but it’s just a normal suburban house not a mansion.
I once had a brief conversation with Obama and shook his hand, but that was years before he was president. It was just after he became the junior senator from Illinois. He was just coming in from a smoking break outside the Illinois Center on Michigan Avenue - I think he was there for an interview with Fox or something. Asked if I had voted for him and I said no, I lived in Indiana, but wished him luck with his career and said if down the line the opportunity to vote for him came up I’d certainly consider him.
I dunno - does that count?
10 feet from Dubya. I was on the side of the road when his motorcade drove by, and he actually had his window down and was looking out (I can’t swear he didn’t have his head out the window panting, but I don’t think he did). This was in about 2003 on a back road near the airport, so I assume he thought it was deserted and safe to roll down the window.
I was in DC last week and had hopes of running into Obama. I was prepared and knew what I was going to say, I was going to ask if he could get me Zach Galifianakis’ autograph.
Yes, since a number of people have asked, if you met them before or after their tenure, that counts; especially so if you happened to witness them doing something scandalous. 
I’ve never been really close to a head of state. When Bill Clinton came to our city those at my workplace had a fantastic close view of Air Force One as it banked overhead on it’s approach to the airport. So, half a mile to a mile away?
I may have shaken hands with President Vigdis Finn Bogadottir of Iceland, but if not, I at least stood just a few feet from her. I definitely remember George Bush I riding by in a car (motorcade) while I stood on the sidewalk, and I’ve been in the same city at the same time as a bunch of others.
Another Head of Government but not Head of State…
I was alone in an elevator with McKeeva Bush, who was Leader of Government Business of the Cayman Islands at the time. The elevators in the old Government Administration Building were ridiculously small and it was not unusual to find yourself sharing a lift with one of the politicos.
I’ve also met 3 governors of the Cayman Islands. They are the Queen’s appointed representative. I met one governor while he was getting out of the shower. We were locked down in a shared office during a hurricane.
Reagan gave the commencement address at Notre Dame in 1981 (I believe it was his first public appearance after being shot by John Hinckley 7 weeks before). My brother and I drove up to the South Bend IN airport to see him. We were never closer than about 100-200 yards. He disembarked Air Force One, waved to the crowd, got in a limo and off went the motorcade.
I was at an Obama rally in Albuquerque in 2008, but he wasn’t president yet. I was maybe 200 feet from the stage.
A couple of times 10 feet or so away from Queen Elizabeth.
I made Pierre Trudeau wait to take off when I landed a Cessna single-engine putt-putt in front of his jet. The PM isn’t the head of state, but, well, that was more fun than gazing at my liege.
I have a picture of the Lieutenant Governor of Saskatchewan holding the Piper Cub as a wee bairn, at the Canada Day garden party in the grounds of Government House. His Honour was Her Majesty’s representative in Saskatchewan, so deputy of the provincial head of state
I once shook hands with Sir Zelman Cowan who was the Governor General at the time in Australia (Queen’s rep in Australia)
Handed Queen Elizabeth a bunch of flowers as a Cub. (Boy Scout)
Met Paul Keating when he was PM of Australia, seemed like a good bloke.
But my biggest was chatting to Dame Elisabeth Murdoch and lo and behold but her son walks in and says g’day! (Rupert) He is the head of the fourth estate so in some respects he is a head of state!
oops also forgot I shook hands with Bill Clinton at a conference, this was after he left the office though.