After a few years of contacting webmasters for link requests and (previously) link exchanges, I've tried several approaches. While I've had success using the roles of a SEO professional, the client themselves, or a brand enthusiast, I've also had some failures.
Let's look at strategies for each of these three approaches, as well as some of the responses you may run into.
As the SEO Professional
If you choose to contact the webmaster of a site as an Internet marketing specialist, link builder, or other SEO professional, there are a few things you have to be aware of.
For starters, website owners will assume that you're getting paid for your services for your client; hence they will want you to pay them for the link.
Also, the worst case scenario is if you somehow offend the webmaster enough (this is especially for those who send automated requests), then you might find your name, company name, and client name linked together in a less than friendly post or write up.
Now what's the benefit of asking for a link as a SEO? If the website owner likes your suggestion, you may be able to form a good relationship with them. Then, later down the road if you have another link that also fits their website, it will be much easier to approach them and secure that link as well.
As the Client
If you're building links for a client, your next option would be to act as its representative, perhaps as a part of their marketing department.
The best scenario is to get an e-mail address from the client's domain, with firstname.lastname@example.org. Second best is to get the client's permission to use a brand based e-mail with a free account, like email@example.com.
Representing the client themselves in an e-mail can work especially well if you're targeting high quality links on official sites (e.g., .edu and .gov). It also seems to come off as more sincere when you contact webmasters.
One side benefit of a good link pitch written as if it were from the client: someone may be introduced to the client for the first time. Although they might not be interested in a link, they might be interested in purchasing some of the client's products. If you're targeting your link requests to related sites (like you should be), this may happen more times than not.
Another important point is that anything you say while acting as your client's representative can be held against your client. Don't get into an e-mail sparring match with someone who could've turned out to be a potential client or business partner.
Most importantly, avoid spamming if you use your client's domain!
As the Brand Advocate
Lastly, you can try contacting webmasters from the approach of someone who loves a particular brand. So if the website is on fashion, and they list a bunch of different stores but not the one you're building links for, you e-mail them to compliment them on what a great site they have, mention that you're a particular fan of XOXO, and you want to know why it's not on their list in hopes they'll add it.
One downside of the brand advocate approach is that this contact type should have little to no knowledge of SEO, which means no anchor text suggestions.
Your e-mail should look like it was sent by a typical mom. So only include the URL -- and maybe the store or product name. Let the webmaster take it from there.
The Key to Success
No matter who you choose to contact the site as, the key is to make every link request a good one. Detail why the link is relevant and beneficial for the webmaster to add to their site.
Also, try to personalize your e-mails with a specific name, not just "Dear Webmaster..." If you make the link request valuable to them, then you're more likely to acquire it!
Your Approach to Communicating with Webmasters
Do you contact webmasters as a SEO professional, a representative of the client, or as a brand advocate? What benefits have you seen from your approach, and what issues have you run into? What advice would you give when it comes to contacting different types of sites?