I've been running a Debian GNU/Linux system since 1996 and have been fiddling and experimenting ever since. I've also been lucky enough to hold some pretty high-flyin' sysadmin positions at big globally sprawling companies. These two things have given me the opportunity to use, administer, configure & seriously tweak a huge variety of different services and features running on a unix system.

Here are some ideas for services aimed at power users and developers that are almost impossible to find amongst the usual offerings of traditional hosting companies,

• Secure SMTP -- send your email from your email program using SSL. Most email programs actually support this but almost no-one knows about it. If you send email from work and aren't otherwise encrypting it your boss/admin could be reading it. (Think about that next time you send out résumés on the clock...)
• SMTP AUTH -- send your email from anywhere. Most SMTP servers & ISPs require you to send email from their machines which usually means one of their email addresses, not from the cool domain you own. This system of authenticated SMTP allows you to associate a username/password with the outgoing SMTP so you could send email from anywhere, using whatever email address you liked.
• Secure HTTPS proxy -- browse the web using SSL. Prevent sniffing and having someone profile your browsing habits (that's right, your company knows you're reading that porn!)
• rsync -- rsync (rsync home page) is an efficient, compressible file replication system. Uses are numerous: from backups to mail synchronization to distributing source code. One idea could be to edit your website locally on your machine and then rsync it with a hosted site here. This is, once set up, vastly less hassle, time- & bandwidth-consuming than FTP which just doesn't support file synchronization, but is about the only way to get your stuff onto a site with 99.999% of ISPs.
• LDAP -- maintain your address books online with a Web form and LDAP server. Bingo, roaming profile: have your address book and contacts everywhere you go, accessible from any machine. Pretty much all email clients support LDAP and make good use of it (fuzzy matching, search etc).
• Apache -- need your own custom authentication scheme for? Custom content handler? You will not find a commercial ISP anywhere who would let you install your own module to futz with Apache's request cycle without operating your own machine (at least, I've never heard of it). Most of them are pretty restrictive about even installing CGI scripts!
• Oracle, Dynamo, etc -- development versions (i.e. full versions but don't use them commercially) of major software products to play with.
• You name it -- if you have an idea, let's talk!