If a tree removal company is reputable, you won't be their first client. It's perfectly acceptable to ask for references on your initial call, and if a removal company won't provide referrals, it's time to move on.
Some types of tree removal equipment are better than others, and a removal company might need special tools to get your particular job done. On your first conversation with a prospective removal company, make sure that you clearly express the nature of the job you want accomplished, and receive assurances that the tools that the company has at their disposal will cut it. For instance, if a removal company doesn't have a crane, their reach is significantly limited.
Always ask for an estimate up-front. Even if a company provides you with an estimate without hesitation, make sure that there aren't any hidden costs.
While the trees in your backyard are good for the environment and look beautiful, they could present a danger to your home under the wrong circumstances. If you live in an area where fires are common or a rotted out tree is threatening to fall over, you'll need to have one or more trees removed, and this task is beyond the capabilities of the average homeowner.