There are many possible reasons; here's a list of the common one:
- Bids may not be high enough to show your ad frequently, or in the first 3 positions, first page results, or not at all; this can due to keyword quality scores being too low, or if they were to show it would exceed the daily budget.
- The ad may not have been approved, which could be due to one of many AdWords policies e.g. copyright, adult content.
- The budget may not be sufficient/daily budget exhausted early in the day, or the payment may have been declined.
- The location targeting could be set to a location or radius, which you are searching outside of.
- The ads may run on a schedule e.g. on certain days, or during set hours of the day.
- Searching for your own ads on Google - if you repeatedly search for your own ad on Google Search but never click on it, you may stop seeing it. That's because Google's system recognises your computer and stops showing you ads that it thinks you aren't interested in (this is also a preventative measure to try stop e.g. spammers/competition from continuously searching your ads and/or clicking on them).**
- Your account may be under review for security measures e.g. verifying billing information, usually soon after the campaign has just been launched.
**Important to search your own ads using the ad preview tool and diagnosis tool: http://www.google.com/