This is a common problem, but really not a big deal. I've usually heard it called "toe overlap". I have it on all my bikes.
Basically, it's a bit shocking the first time it happens, but you get used to it. It's no big deal. If you're simply aware that it can happen at slow speeds, you'll avoid it easily enough. Since it can only happen at slow speeds, it's not particularly dangerous.
It's most common on racing-style road bikes due to their short wheelbase or on smaller frame bikes. Big tires and/or fenders can make it more likely. Big feet and shoes that stick forward of your toes very far also make it more likely.
Possible solutions include:
- Try not to worry about it. It's usually just an annoyance and you get used to it pretty quickly.
- Don't go slow (can't turn the wheel far enough for it to be a problem unless you're going slow).
- When going slow and making a sharp turn, pay attention to where your feet are.
- Don't pedal while turning
- Pump the pedals instead of normal pedaling, so that only your inside foot goes forward
- Get your feet into a good position (outside foot just below where the pedal overlap happens) as you start to turn.
- Also pay attention when starting from a stop.
- Pedal with the ball of your foot over the spindle of the pedal. This is generally considered the "correct" place, and leaves your foot only going a little forward of the pedal. Some beginners put the arch of their foot on the pedal, which is likely to be uncomfortable on platform pedals, and puts your foot more forward.
- Maybe slide your foot back a bit as you're making a slow turn, so that you pedal with your toes instead. I find this uncomfortable, but it's tolerable for a few seconds.
- When you're shopping for bikes, look at how much toe overlap there is. You don't even need to ride the bike, you can tell by putting the pedal forward, putting a foot on the pedal at about the right position, and turning the handlebars.
- Smaller riders may find that bikes with smaller wheels give them less toe overlap. 650b or 26" instead of 700c?
- Really, don't worry about it too much.