Inspired by a current thread on how close one can get to the Pope, I’m wondering what is the closest distance members of the Doperverse have ever been to a Head of State (and who that may have been).
Mine are been pretty pathetic: I once watched Francois Mitterand get on his helicopter from about 90 feet away, and another time was momentarily within ten feet of Margaret Thatcher as her car went by on the street. Maybe it doesn’t count if there’s a layer of armor and bullet-proof glass in between.
I’m sure, however, there are members of this board who have been close enough to shake hands with the President, or perhaps throw a shoe at him, depending. Here’s your chance to brag.
Not a winner: I was about 300 yds. from Dubya when he spoke at a high school adjacent to where I work.
I was within a few inches of Nixon.
I’ve shaken hands with two Presidents of Panama while they were in office, and been within 20 feet of another. I’ve met another former president, and had lunch with a current Vice President of Panama in Washington in the early 1990s. I’m on a first-name basis with one of the current candidates for president, having known him for about 25 years (but he’s probably not going to win).
But Panama is a pretty small country, with a population of only 3 million. Shaking hands with the President is kind of like meeting the mayor of Philadelphia. 
I can’t be sure, but once when I was visiting DC near the White House, a limo and motorcade pulled out right in front of me. Could have been Bill Clinton, but I couldn’t see inside.
I’ve been at USNO when the VP departed in Marine 2. Does that count?
I was in Rome in one of the mega-audiences with Pope Paul in '72, and I think he walked past within 30 feet of our group.
Next closest was when I worked in the Pentagon - I was looking out the window on the 4th floor when Reagan was in the courtyard pinning a medal on a soldier. I couldn’t make out which blurry blob he was. But they tell me he was down there.
I was bike riding with my family along a trail when we passed (riding in the opposite direction) Bill Clinton. None of us noticed except my mom, who then stopped and made me crash into her. 
But this was after his Presidency, so it might not count.
ETA: Oh, and recently I was in DC by the White house and Joe Biden was surrounded by a big fleet of Secret Service men. Didn’t actually see him, though.
I once exchanged pleasantries with Pierre Elliot Trudeau. In the middle of St. Catherine st, downtown Montreal, on a Satuday night. He was simply walking down the sidewalk, I looked up and there he was. I smiled, he smiled, we shook hands, and kept going. The man had presence.
Also, had dinner sitting at table next to Newt Gingrich. After he was house speaker. He’s taller than I expected.
When I worked in events, I had a dinner that included five sitting heads of state (US, UK, Germany, France, Italy). Banquet room that held about 150 guests.
The more interesting part was working with five security details in the days leading up to the dinner! I was fascinated by what things were the same, what were different, what some countries felt strongly about, etc.
Assuming he was in the White House at the time, then he was about 100-200 yards away from me when I walked on Pennsylvania Avenue.
I went to a speech by Bill Clinton during his reelection campaign in '96. After it was over and people were starting to dissipate, I saw a little walkway that was set off by police barricades. I had a hunch and walked over to it. Yep, it was the handshake line. Got a brief shake as he was moving past.
About ten feet from Clinton; he was shaking hands down the line and turned back about three people from me. DiFi was following up for him, but I remember the guys on the roofs (it was an Air Force Base, out on the flight line) with scopes the size of top hats better than I remember her.
And I was in the audience of Willie Brown’s short-lived talk show and chatted with him after taping, but he was only shadow ruler of California.
I shook hands and had my picture taken with a presidential nominee, but that doesn’t count.
I wonder if any female Dopers were a congressional aid, or white house staffer, during the Clinton administration.
I once shook hands with Gerald Ford at a public crowd event.
I have met and conversed with the Presidents Ford, Carter, Reagan, both Bush I and Bush II, and Clinton. In fact, Presidents Nixon and Obama are the only ones in my lifetime who I haven’t met while they were in office. (I am told Nixon rubbed my head as he passed in a parade, but can’t vouch for it.)
I sat in the Presidential box at the Kennedy Center with Mr. Reagan for Lilly Tomlin’s one-woman show “The Search for Intelligent Life in the Universe.” It was awkward. He was horrified by a lot of it, and we were all struggling to hide our great enjoyment.
I sat at table for lunch with Siaka Stevens (and about ten other people) in his last year as President of Sierra Leone.
I met Tony Blair while he was Prime Minister, John Major before he was Prime Minister, and Margaret Thatcher after she left office.
All of this is fairly normal where I live, though. I just happened to have a very active social life in the late 80’s and early 90’s, and around here that means embassy parties. None of those people were there to meet me, and I doubt any of them would remember me. 
I shook hands with President Ford at the dedication of the Stanford Law School building in 1975. If you scroll down to the fourth page of this .pdf (which is actually labeled page 2), you can see my sister and me sitting in the front row directly in front of the podium.
I also had a book signed by President Clinton after his presidency. I can’t remember if he shook my hand.
Walter Mondale was a familiar face around my home town and I attended a party for him when I was a toddler. Don’t know what it was. Perhaps his college graduation celebration.
My daughter and I may have been within 20 feet of the POTUS a few weeks back. We were attempting to cross Broad Street in Falls Church VA and a policeman had just stopped all traffic in the intersection - but saw us waiting to cross on foot and waved us through quickly. I figured something was up, so we waited by the road - and sure enough there were a few black cars with lights flashing, followed by a black car with all the windows darkened, followed by a few more black cars.
Whether it was the POTUS, FLOTUS or someone else entirely, we’ll never know.
Aside from that, we’ve certainly been within a few blocks of him any number of times, including a recent walk just past one of the White House fences.
My son shook Obama’s hand at a rally back in 2007 or early 2008, before he’d officially declared his candidacy, so I guess that doesn’t count.