Different programs in the same alliance can have very different requirements for the same tier of elite status as recognized by the alliance. For example, Aegean requires less than UA or LH for *Gold. However, some programs require that you fly a small number of segments on their airline (maybe including codeshares of joint venture partners, so read the fine print) or spend a certain amount on their fares.

Look also at expiration policies for redeemable miles in various programs. For example, DL miles currently don't expire until you do, while SQ miles absolutely expire after two or three years regardless of continuing activity in your account. In some programs, having a certain credit card or making a very minor purchase can keep your miles alive.

You should have enough FF accounts in order to avoid ever taking a flight where you cannot credit miles to some program, but you should also concentrate your miles on as few different programs as possible. For most people, this means one account per alliance, with it often being wise to pick the carrier within each alliance that you fly the most, but there are many exceptions to this general rule, some of which were pointed out above by Efrem.

ADDED: If you haven't already done so, you should read your company's travel policy very carefully. You might have more or less flexibility to pick flights than you think. Also, don't forget about hotel and possibly rental car programs too.