I'm fairly young (about 30), and I ride my bike almost every day (commuting) and try to push myself, so I'm in decent shape. I also like to do longer rides, which involve riding steep roads up a nearby mountain. Even in my granny gear, the roads are steep and long enough to get my heart rate very high. I don't know exactly how high because I don't have a heart rate monitor, but it's high enough that I absolutely have to stop along the way.
Should I be concerned about overexertion? If so, are there any signs in particular I should look out for? I just want to make sure to avoid dangerous activity. If you're in good shape, is it safe to exert yourself as much as you're able to?