Large organizations typically are all about the benjamins. (Some are not ONLY about the benjamins, but ultimately in the end, at least enough benjamins to stay afloat).
If you want to do well in a company like this you need to think of ways to do one of two things.
1. Make them more money.
This is where having ideas for new products and ways to bring in more revenue come into play. Look for areas of opportunity, what things do potential customers struggle with daily, that you/your company can fill the hole with a "new" product. Sometimes this happens because you've found something that you do daily that could be made easier and boom new idea. I think this is sort of how Trello came along, it was frustrating keeping track of where everyone was on projects/etc, and Fog Creek came up with something to make it easy. Now it's a product their customers can use.
2. Save them more money.
I HATE sitting around on my butt doing things that computers should already be doing. Working in a software company, there are too many times I have to watch test scripts run and do things when they pause. Finding ways to "fix" these pauses, so you don't have to have your butt in a seat is a money saver, and companies like that. One of my latest "money savers" was writing a wrapper that used auto hot key, so now whenever a script needs the user (note: me/collegues) to do something, we just have the auto hot key utility do it for us. It saves engineer hours, and sanity (if you're anything like me you hate the idea of wasting your precious time sitting and waiting for some "dull" event to occur just so you can do some dull thing to make the next event occur!).
How do you do these things?
Always be cognizant of your surroundings, look for opportunities. If you see something you think would be neat to try, go for it. If you have to do it a little on your own time to get a proof of concept by all means. Now if you're spending months of it, I would at least bring the idea up to see if it sparks interest, and possibly get paid specifically to do it (otherwise you're giving away your time to a company that has no vested interest in you other than "Wishes to avoid training someone new" which I may talk about someday).
Every day when I sit down and look at what I'm doing, I think to myself, how can I avoid having to do things that I don't find fulfilling, I can't always automate things, but I'll be darned if I don't try whenever I think it makes sense. We are engineers, not monkeys, and to be honest making us sit in front of a PC and act like monkeys just doesn't make sense. So lets do something about it, make a change and see what happens. I think you'll find that if you make it simple (easy for everyone to use), and it works, you'll at least attract some attention, and maybe even some more interesting projects. I have always said, you make the work you do what you want it to be. So make it!