Linking power, link popularity, and anchor text all have their place. However, site content sets the standard. If a site is good, it attracts links. If it's not, it doesn't. The quality of the content is related to the number of links it attracts.
Getting Feedback.
Things creating a negative response with link requests include:
Over-emphasizing the benefits
e.g. "If you link to us, it's to our mutual benefit", "I'm sure you'll get a lot of traffic from our link", etc. Any talk stressing how getting what you want benefits them, creates suspicion. It sounds like cheap talk from a huckster.
Long messages
Other webmasters have seen and sent messages like yours many times before. They know what you want. Be polite and to the point. All you really need to say is, "Please could you link to us". You get either a yes or no, depending on your site.
Repeat messages
Do not worry about people ignoring your message. Assume they saw it the first time. Don't send it again, as this is just annoying. Many people make decisions based on how they feel. If you want their help, don't make them feel bad.
Personalized messages
Many say you should send personalized messages. However, there are those who don't really like them. Sometimes it appears obvious you're trying to cover up the fact you've sent a similar message to 499 other folks. Attaching a name, website URLs, and inquiring about my relatives' health doesn't really change anything.
If it's personal, it'll be obvious it's personal. If it's been sent to multiple recipients, it'll be similarly obvious. As before, be short, simple, and open about the fact you'd like a link.
Followup/Warning messages
This is the same as sending multiple messages. It's just a different time scale. Your message was sent. Assume it has been read. Repeating yourself creates a negative impression. This is especially true in this age of spam.
Messages saying "I've already linked to you so..."
While links are the goal, this says, "I helped you so now you've gotta help me". It takes away choice and creates a negative feeling. Besides, in many cases, the links associated with these types of requests aren't so great anyway.
Link Automation.
Most of these points stem in part from email templates found in link development software. Like all such tools, it's possible to use them legitimately. However, they are often used improperly. Webmasters, with any experience, are accustomed to these templated requests.
Suggestions.
One good thing to try is link code. Create a links directory with descriptions for each site. You avoid having to write them each time.
Conclusion.
The following are key points to remember when creating your link requests.
Keep it short.
Lose the chaff. Simply ask for the link.
Give a small amount of clear, honest information about your site. No marketing-speak.
Include link code.
If you've made a good site you'll get more links and more traffic. More importantly, you are sending considerate and effective link requests.