What's interesting is that we can get paid for travel to other customer sites of our employers when using personal vehicles (up to $.535/mile per IRS guidelines[0]), but not to go to our actual workplaces.
If you have a home office and commute to a client site you can claim it as a deduction at tax time. Outside of that I do know of some employers who do reimburse mileage as long as it is filed and more than 20 miles but that is rare.