Record to tape: Many engineers still prefer the sound of analogue tape, praising it's warm, fat sound. Although most of us don't have access to a professional 2-inch recorder, we probably all have a cassette recorder lying around. Try bouncing down some drum loops, feeding the tape a nice hot level.
Run it through an amp: Guitar amps aren't just for guitars! Beats, synths, even vocals can all benefit from anything from subtle thickening to total overdrive. As well as the tweaking the sound via the amp you can also experiment with different microphone techniques.
Real reverb: Back before quality digital reverbs it wasn't uncommon for a studio to have one or more echo chambers - rooms specifically designed to be reverberant. A speaker and microphone setup would be permanently set up with a send and return from the mixing desk. If you've got a tiled bathroom or even a metal bin, then you've the makings of your very own echo chamber!
Old gear: 12Bit samplers, early digital reverbs, old EQs all have a character of their own and could help you create a signature sound. Sometimes the worse the condition, the more interesting the results!
Cheap gear: Cheap electronic instruments tend to produce a very raw sound. Inexpensive keyboards in particular feature very basic synthesis that can often cut through a track and sound more up-front then their more complex and expensive counterparts. So it you've got an old Casio lying around gathering dust, turn it on and have a search through some of the presets, you might be pleasantly surprised.
Guitar effects pedal: Again, just because it says guitar on the box doesn't mean you can't run other stuff through it. Stomp boxes in particular are a pretty inexpensive (and fun) means to introduce some truly transformative processing to your mix And because your hands won't be occupied with guitar strings you can indulge in some real-time tweaking of the various controls. Take a look at the massive range available from manufacturers like Behringer with everything from flangers to filters starting from under £20 per unit.
Noise: why not use noise itself? Record some hiss and stick it under your beat, maybe with a noise gate or side-chained compressor so that it pumps with the track. Or use it as a standalone instrument bringing it in like a reverse cymbal or and filtering it to create a unique morphing texture.