Pointers:

If you are adding additional facts or information:

as well, and, additionally, furthermore, also, too, in addition, another, besides, moreover

If you are trying to indicate the order of a sequence of events:

first of all, meanwhile, followed by, then, next, before, after, last, finally, one month later, one year later, etc.

If you are trying to list things in order of importance:

first, second etc., next, last, finally, more importantly, more significantly, above all, primarily

If you are trying to connect one idea to a fact or illustration:

for example, for instance, to illustrate, this can be seen

To indicate an effect or result:

as a result, thus, consequently, eventually, therefore,

To indicate that one idea is the opposite of another:

nonetheless, however, yet, but, though, on the other hand, although, even though, in contrast, unlike, differing from, on the contrary, instead, whereas, nevertheless, despite, regardless of

When comparing one thing to another:

In a different sense, similarly, likewise, similar to, like, just as, conversely.

 From ESSAYS THAT WILL GET YOU INTO COLLEGE, by Amy Burnham, Daniel Kaufman, and Chris Dowhan.
Copyright 1998 by Dan Kaufman.  Reprinted by arrangement with Barron's Educational Series, Inc.