Not every link you request requires giving a link back. Sometimes it is cheaper and more efficient to just to go target higher quality links. Sometimes you can just request a link and get it by being personal and empathetic. Other times links may require payment.
The best way to go about acquiring links is to be as personal about it as you can. Look around their web site and try to find personal information. The more you find, the better you are.
When e-mailing them, try to submit it to the person who runs the site, not a general info submission. If you can state where your link should go on their site and how it would improve their user experience, you stand a good chance of getting a link.
Off-topic, somewhat personal statements showing you share similar interests may make you seem more human and more connected with them and will make it easier to get links. For instance, if you found out that I like peanut butter, somehow mentioning that or joking about it in the e-mail will make me far more likely to link to your site.