Mike,
Great topic for a post, especially a first post!
I'm agnostic, more or less, but I tend to think of myself as a "hopeful agnostic". That is, I'm not sure if there's a God or not, but I sort of lean in the direction of thinking there is, and I definitely
hope there is. I've prayed that God would show me some kind of sign of its existence, but the problem is that since I know I hope there is a God, I'm prone to interpreting any possible sign as simply my own wishful thinking. Which it may very well be, but then again it might also be an actual sign from God, and how am I to tell the difference? I know this isn't exactly the same as your experience, since you evidently do believe in God, but I do think it's similar.
I've had lots of small experiences like the one you had with the license plate. In fact, one thing that happened to me a number of times also involved license plates. At the time, I lived at home with my Dad and sister, and my sis and I spent the day with my Mom once a week (my parents were divorced, and we lived with my Dad, but my Mom lived about 1/2 hour drive away). I was going through some fairly serious depression, for a variety of reasons, and felt that I wanted God to show me some kind of sign of hope. I don't know if you know French at all, but the past tense of the word "believe" in French is "cru". Well, I started seeing "cru" all over the place in people's license plates, for a few months at least. Admittedly, this could simply be coincidence, but in any case it helped me.
Other times I've found bits of paper with things written on them that were either notes thrown at me by God, lol, or else amazing & amusing coincidence. For example, I used to work at a bookshop in a mall, and I was at work one day and feeling very down. I was straightening the poetry section, and saw a crumpled up piece of white paper on the floor, so I picked it up, and being nosy I wanted to see if anything was written on it before I threw it out. For the life of me I can't remember exactly what it said (I wish I could, but this was over 10 years ago), but I do know that it was something encouraging, like an affirmation of some kind only it wasn't corny/cheesy, and it was the only thing written on the paper, there was no other context. Yes, someone could have written it for themselves to make themselves feel better, and then just dropped it in our store accidentally -- in fact, that probably is what happened. Still, who's to say that if there's a God, God didn't plan it that way for me to find? Again, either way, it helped.
Another time -- more recently, this, about 7 years ago, and in the town where I live now -- I was walking along the street in town, feeling lonely, and written on the dark red brick facade of a shop I glanced at as I walked past someone had written something like "You saw the beauty, and you understood, and you were glad" in white chalk.?!?!?

Again, it was entirely alone, out of any other context.
About a year ago I asked, rather randomly, that if there was a God would God please show me a blue star. Not an actual astral body, I mean a star representation -- you know, like you would draw. In blue. Every now and then I'd think of it, and look around me, but no blue star. Then one day my boyfriend and I were driving, and I wasn't thinking at all about God or the star, when I looked out the window and saw a
huge blue star painted on the side of a building across the highway, for no reason that I could see (e.g., it wasn't a club called "The Blue Star", or anything like that). The star looked a bit faded, weathered as though it had been there a while. I was surprised and a little flabbergasted.
I hadn't actually made this connection until now, but -- where my boyfriend and I were driving that day was to the vet. A co-worker and I had found a cat at the parking garage at work, and though we asked around we couldn't find the owner, and couldn't find an animal shelter open to take him. We couldn't leave him in a parking garage, as he might get run over, so finally I took him home for the night. I was thinking about keeping him, and started looking for vets to have him checked out, get his shots, etc. He was a nice cat, quite affectionate, but you know how cats sometimes will let you pet them for 20 minutes and then when they decide that's enough they nip or scratch you? Or how they will hide behind a piece of furniture until you walk by, the run out and nip you and run away? Well, he nipped my calf and my knee. Not badly, only one drew blood, and then only a drop, and it didn't hurt -- but the problem was, I didn't know anything about this cat, if he'd had his shots, etc. So we were taking him to the vet to get him tested for rabies and other diseases, to be sure he didn't pass anything on to me. Long story short(ish) -- I didn't know you can't test for rabies unless you cut into the brain, so the vet had to put the cat to sleep and do that. I was extremely upset and bawling, as was my boyfriend. It was AWFUL. But now the connection that I'm making is that is was on
that car ride that I saw the blue star I'd asked for. Which makes me feel better
now.
I hope I haven't hijacked your thread, but once I got started I kept remembering more stuff. There are probably other things as well, but it's 11.30 pm and I've got to have a shower and go to bed.
Thanks for starting this thread!