I've had water seep through my basement window quite a few times in the past two years. While I've done what I can to prevent this (clean gutters, divert downspouts) water stills builds up within my basement window well occasionally, and eventually seeps into the basement - wrecking havoc on my day.
Last year, I added a bilge pump to the window well which was powered by a couple of 6V lantern batteries. This worked - until the batteries died.
So - I decided to up my power source to an AGM (absorbed glass mat) Lead Acid battery which gets charged via a solar cell.
DISCLAIMER: Be careful when using tools - protect your eyes - think twice before doing anything. With batteries, you can't unplug them - they're always 'hot' - watch where you put your tools - avoid possibly shorting out the terminals. Keep the protective terminal covers on the battery until you actually connect it to your circuit, and when you do, make sure a fuse is the first thing to get connected. Batteries can be dangerous - they can explode - leak acid.
Step 1: The Bilge Pump
I purchased the bilge pump and float switch at a wally world - I think it was for around $35-50. Sorry for the lack of detail here - did this at 3am after cleaning out my basement all night :(.
The bilge pump is designed for small boats to expel water within their hauls and keep them afloat, it's not an industrial pump by any means. The accompanying switch is a small float switch which closes the circuit once the water level is at a certain height.