I haven't been very physically active in the last few years. Several years ago I had some of the strongest legs of anyone I've ever known and probably the same endurance. Even though I wasn't extremly fit, I could push myself very hard beyond my "limits".
Six years ago I joined the Marines while in High School and was in delayed entry for about 7 months. We had to do physical fitness once a month on the second Saturdays. The first time I ran the 1.5 mile run I pushed myself so hard I puked several times after the run. Within about 3 minutes of the run my legs refused to move and I had to force myself to keep going. I went through about 12 minutes more of that and finished the run. After that I ran more and got very fit and even though I found it hard to run 1.5 miles I was able to do it and didn't have a problem with my legs refusing to move after a certain point.
Now, it seems I am back to that point. I haven't done a lot of physical activities in a few years and I decided to get a bike. After a few minutes my legs feel like they are locking up and I can't stand up on the bike and pedal so I have to sit down. I know it takes time to get back in shape, but I am sure there are "warm-ups" or pointers a lot of you can give to getting back in shape.
There are most likely "wrong" ways about pushing yourself when you are out of shape and "better" ways of doing it also.
I think it's completely fine to push yourself beyond your "limits" because it helps you get in shape quicker and I think if you don't push yourself and stop when you begin to get tired you won't make progress, but like I said, there are "wrong" ways to do it too :-P.
I asked for a road bike for Christmas but since I am out of a job right now I can't afford it, nor could my parents so I ended up with a mountain bike. So, right now I guess I am mostly confined to off-road or short-distance rides (my brother found a used Diamondback mountain bike).