We've all experienced this in one way or another. Replacing your mobile phone or smartphone with a newer model means the old device ends up in a drawer for months (or why not years). Of course, there's always the chance to give it to someone or even sell it for a few bucks if it's in good condition, but we have several alternatives that let us take advantage of its features even when the rest of the world says it should be recycled.
Alright, let's say you've just retired your aged Android 2.x smartphone in favor of a new device. Better performance, optimized interface, more compatible apps... you can see the benefits almost immediately. However, there's nothing strange about the previous phone, is there? Technical problems in phones can be as common (or more) as on a desktop computer, but a good number of the phones that are discarded by their owners still work without issues. That phone now holds enormous DIY potential. You can try everything you've considered in the past but always put off for fear of damaging it. With that in mind... if its role as a communication medium is already taken, why not turn it into something else?
Audio Equipment
For example, over the weekend I set out to restore an old Motorola i856 that I had in a drawer. After tracking down its firmware and returning it to its original factory state (which required a virtual Windows XP environment due to the age of its software), all I had left to do was load music onto its microSD card and connect external speakers. You might be tempted to place MP3s at maximum quality, but when dealing with limited hardware, it's more logical to make a small compromise here. After all, if the source of the music is good (lossless files, say), the conversion will sound very good. Now, don't let this case stop you. You can always make a kind of wooden or plastic casing, with guides for the cables, and turn it into something more permanent.
Chromecast!
The Chromecast has proven to be a more than interesting accessory, but in general, Google products tend to need an external companion to make full use of their capabilities. If you now have a spare smartphone... I think the next step is obvious. Assuming the phone has at least Android 4.0.3 or a compatible iOS build (I think it's 7.0 at the moment, and support extends to iPod Touch), sending content from the device to the Chromecast and your TV is an excellent idea. If you have a tablet, don't worry, this is also within your reach.
Digital Photo Frame - Clock
Unless a destroyed screen wasn't the reason you retired your phone, with the right app and a few configuration tweaks it can cycle through photos of the moments we consider most important. Why would you buy a digital frame (which in some cases can be worth hundreds of dollars) when a smartphone can do a similar job? As far as apps go, several sites point to Dayframe, though it requires Android 4.1 as a minimum.
IP Camera - Baby Monitor
WiFi connectivity on a mobile phone predates the smartphone itself, so it's not far-fetched to assume that your secondary device can connect to a local network. So why not add an IP camera to that same network and use the smartphone as a "window"? From basic surveillance over the front door to what's happening in your little one's room, an extra bit of peace of mind using an extra phone doesn't sound bad at all. There are even apps that transform the smartphone into a monitor, allowing you to monitor the situation from your new device.
Rooting - Jailbreaking
We all know this very well: mobile operating systems are sandboxes. Either you play by their rules, or you must leave the box. That said... why don't we leave? Performing a root process on Android or jailbreaking iOS requires some prior research, but since you're working on a secondary device that currently has no use... let's say you can take the risk. Jailbreaking iOS enables the installation of a whole parallel market of apps that don't exist on the official App Store, while rooting Android presents us with the magic of firmware changes, with projects like Cyanogenmod and similar.
Needless to say, we've barely scratched the surface here. A mobile phone doesn't stop being a computer, and all it's waiting for is an optimized role that fits its available resources. Moreover, if the device already carries a couple of years on its back, finding documentation or accessories like batteries should be relatively simple. Don't let your phone sleep, do something with it. Good luck!