I can name a few things:
- DNS. It can be low end because you usually have more than one, so the other one can act as a replacement while you get the first one up. Also, DNS doesn't require so much server resources, so low end box can suffice
- Backup. If the box has good network and a lot of storage, you can use it to backup your data. If you use rsync, then even better because you only copy over the changes that were made after the last backup
- Website. Simple PHP website or a forum can be hosted on a low end box and still serve decent amount of traffic
- Email. Mail server can also be hosted on a low end box and you can use it as a SMTP server for email sending
- Raw data storage. You may have some bulk, raw data that you need to store somewhere but only if that data is not being read/written often
So I think the general rule is that you can use low end box if the thing you need it for won't be accessed/used regularly and concurrently by a lot of people.