One of the biggest factors determining your link request success rate will be how you go about finding link targets. It's no good sending out emails randomly; you have to find websites that actively link out to websites like yours. If they are already linking to other websites there has to be a possibility that they can also link to your website. My first step in this process is to run a few custom queries in Google to try and find some potential websites to approach.
To find websites in your niche with links pages try running the following search queries:
your-keyword intitle:links inurl:links
your-keyword intitle:resources inurl:resources
Replace 'keyword' with an appropriate keyword that describes what you are looking for.
As an example, let's assume you run a children's gifts ecommerce website and you want to find children's entertainers websites. Simply search for:
Children's entertainers intitle:links inurl:links
By running this search in Google, you should end up with a nice big list of children's entertainment websites that have links pages; and the ability to link back to your website.
Now you have to find out why they are linking to other websites. Most webmasters have one of a few reasons to link to other businesses; they could be friends, partners, or perhaps they have exchanged links. Finding out the answer to this question is one of the biggest steps towards gaining a link. I personally wouldn't advise you exchange links en masse; you need to find some other reasons for them to link back to you.
If you have enough time available you could offer to provide them with some new content for their website. Perhaps they could benefit from a few guides or an FAQ's page. If they are local then you have the opportunity to offer them recommendations and business leads. The real trick is to find something that will genuinely benefit their business; something that means linking to you makes perfect business sense and is an opportunity that shouldn't be missed!