It entirely depends on what is waiting for me at X time, but you better believe some conscious thought is going into it.
Some examples:
If its an important meeting, its important to show up on time. I don't want to miss anything in the meeting or appear to be disorganized to others. Occasionally I'll show up early to prepare. Occasionally I'll show up late to assert myself (being late says my time is more important than yours which can be detrimental... or a power move).
If you are interviewing or meeting someone new, its important to show up on time. First impressions matter.
If you don't have anything important to do at work until 9:30, its okay to come in at 9:15. Make up the time after. (I'm against 9-5 mentality. I'm a firm believer in flexible schedules. It can also be used to your advantage offering better coverage of staff if some come in early and some later, etc). Some jobs (like the service industry) its imperative to show up on time, but a lot of jobs... it doesn't really matter as long as you get your work done (IT for example).
If its a movie, it depends on the movie (old, new, time of viewing, etc). Some have previews that can buy you an extra 15 minutes, others may have a trouble finding seats which are a big no-no in my opinion, etc.
I never show up to the doctors on time unless its early in the morning/afternoon and their schedule didn't get messed up, you have to fill out paperwork, or its a doctor who runs on time. I usually show up a couple minutes late (gasp!). They are notoriously behind schedule and like I said before, I hate waiting.
My last example is from a date I recently had with my wife. We had a painting class downtown. We had trouble finding parking because it was Sunday (church - no street parking) and the parking garages were closed. It drove my (ISTJ) wife nuts. She didn't want to go in she was so embarassed. My response... I'm paying money for this class, I come when I please. I don't need an excuse to be late to something so trivial.
For the most part though, I'm notoriously on time - neither late nor early unless for good reason.