Tremolo Block: Here's a simple mod popular on many Strats- block your tremolo's inertia block. When you block your tremolo, you will no longer suffer from trem-induced tuning idiocycracies, string flutter when bending notes, or going completely out of tune when you break one string.
This mod is completely reversible and requires no permanent modifications to your guitar. Perfect for beginners to help with tuning stability and great for owners of vintage instruments that want to lose their tremolo without losing the value of their instrument!

Change Pickups: Simple and affordable, try changing your pickups! Yank the bridge single coil and stuff in a humbucker. Don't wanna get a new pickguard or cut the old one? Install a single coil sized stacked humbucker. Like the single coil sound, but not the noise? Put in noiseless single coil style pickups. How about active pickups? Not a lot of dough? How about buying used pickups?
This could go on and on, but the point is, for very little money (sometimes) and little effort, you can drastically, or subtly, change the sound of your instrument.
As with other mods, you can do it yourself, or we can do it for you. Pickup changing is easily undone, but may affect the value of vintage instruments, even after being reversed.

Whammy Bar Tuneup: OK. Maybe you really like your stock Strat trem. Lots of people do, but maybe you want just a tad more performance out of it.
Let's start at the top-
Is your nut adjusted properly? Does it ping when you tune or use the whammy? Maybe it needs to be cleaned or lubed (graphite works great). A new high tech nut made by Graph Tech might help. They also make saddles, too. The Graph Tech material is a lot more slippery than traditional materials, preventing your strings from snagging at these two important contact points when they move with your trem action.
Other things to try are Fender brand Bullet strings, which have specially designed bullet shaped ends to fit the inside shape of Fender tremolo inertia blocks, reducing sticking and drag. You can also try the super-double-secret trick of soldering the windings on the string ball/bullet ends to prevent slippage there!
These are just a few ideas. Others might include varying or adjusting the number or depth of bridge screws (vintage style), chamfering screw holes and spring placement. Experimentation is the key.
Or, you can leave it to us :-)