If you want your phone that is capable of running apps to last for weeks on battery, the big trick is to make sure it doesn't actually run apps for the most part. The second part is to make sure it has good reception. Also, disable any radios you don't need, etc.

If you took a random Android, put in a sim, uninstalled or disabled as many apps as possible, and left it screen off where it had a good view of local towers, you'd have pretty good battery life. It wouldn't be very exciting... but if it just needs to sit in a drawer (hopefully not a metal drawer, see reception issue) and forward a couple sms a week, it'd probably make it through at least one week.

If you go for a model that has a higher capacity battery as a feature, that'll help too.