Q:

Do opposite types in romantic relationships attract?

Is there any scientific truth to the common maxim "opposites attract" when applied to romantic relationships?
I'm not necessarily looking for one blanket answer, though an overall trend or pattern would be helpful as part of a more complete answer.

Here are some related questions that you might consider:

Are there certain "opposite" personality traits (e.g. introversion vs. extraversion, rational vs. emotional decision making, etc.) that are more likely to "attract" than others?
Are there any similar patterns regarding physical characteristics (e.g. height, hair color, athletic ability, etc.)?
Is there any data on the difference between or sameness of people affecting the long-term success of committed relationships?
An evolutionary perspective would also be welcome.  For example, is there any data that suggests that a tendency towards genetic diversity might drive such behavior (if in fact, it does exist)?

If you believe this question is too broad or needs to be clarified in any way, please make suggestions in the comments, and I will address them promptly.  Thanks!

A:

The answer to your question is, for the most part, no:  Opposites do not attract.
Like-minded people attract; that is, the relationships they form are fuller and longer-lasting
than when paired with an opposite-minded partner.  This is despite the fact that people often claim,
in surveys and when asked directly by interviewers, that they would like someone with personality
characteristics different from their own; revealed preference and lived experience show that they
really don't know what they want.
The article, Do People Know What They Want: A Similar or Complementary
Partner?, by a certain Pieternel Dijkstra,
reviews the hypotheses, and the research, better than I could give myself:

With regard to [] “relative” mate preferences two hypotheses have been presented. First, according
  to the “similarity-attraction hypothesis” individuals feel most attracted to potential partners who,
  in important domains, are similar to themselves (e.g., Lucas, Wendorf, and Imamoglu, 2004). Similar
  individuals are assumed to be  attractive because they validate our beliefs about the world and
  ourselves and reduce the  risk of conflicts (e.g., Morry and Gaines, 2005). Not surprisingly
  therefore, similarity between partners contributes to relationship satisfaction (e.g., Lutz-Zois,
  Bradley, Mihalik, and Moorman-Eavers, 2006). Because a happy and long-lasting intimate relationship
  contributes to both psychological and physical health (e.g., Berkman and Syme, 1994), similarity
  between partners increases their own and their offspring’s chances of survival by helping maintain
  (the quality of) the pair bond.
In contrast, according to the “complementarity hypothesis” individuals feel most attracted to
  potential partners who complement them, an  assumption that reflects the saying that “opposites
  attract” (e.g., Antill, 1983). Complementary individuals are assumed to be so attractive because
  they enhance the likelihood that one’s needs will be gratified (e.g., De Raad and Doddema-Winsemius,
  1992). For example, young women who lack economic resources may feel attracted to older men  who
  have acquired economic resources and therefore may be good providers (Eagly and Wood, 1999). In
  addition, from an evolutionary perspective, one might argue that seeking a complementary mate,
  rather than a similar one, may help prevent inbreeding.

Ultimately, this is the punchline (emphasis mine):

Studies on mate selection have consistently found support  for the “similarity attraction”
  hypothesis. Homogamy has been reported for numerous characteristics such as physical attractiveness
  (e.g., White, 1980), attachment style (e.g., Klohnen and Luo, 2003), political and religious
  attitudes (e.g., Luo and Klohnen, 2005), socio-economic background, level of education and IQ (e.g.,
  Bouchard and McGue, 1981). In contrast, support for the “complementarity hypothesis” is much
  scarcer. Although many individuals occasionally feel attracted to “opposites”, attractions  between
  opposites often do not develop into serious intimate relationships and, when they do, these
  relationships often end prematurely (Felmlee, 2001).

There is a particular area where people often do seek partners different from themselves, that's hot in the field of evolutionary psychology, and is extensively researched — that would the major
histocompatability complex, or MHC, in human mate choice.   The MHC is a genomic region which codes for
protein receptors, MHC proteins, which are heavily involved in the immune system and autoimmunity;
the body uses them as antigens so that T cells and NK-cells, our immune's system "policemen", can
recognize foreign elements and differentiate them from "self". To protect against the great
diversity of bacterial and viral invaders, the MHC genome region needs to be highly polymorphic;
that means inbreeding at those loci (by mating with a "more-alike" partner) would be deleterious and
evolutionarily disfavored because inbreeding homogenizes alleles, which in turns means that mating with an "alike" individual would decrease the recognition ability of their offspring to detect pathogens. Thus, research often finds that humans often favor
dissimilar MHC alleles in their mates, which some researchers have hypothesized is mediated through
olfaction.  Here is the abstract of one such study finding these preferences:

Preferences for mates that possess genes dissimilar to one's own at the major histocompatibility
  complex (MHC), a polymorphic group of loci associated with the immune system, have been found in
  mice, birds, fish, and humans. These preferences may help individuals choose genetically compatible
  mates and may adaptively function to prevent inbreeding or to increase heterozy-gosity and thereby
  immunocompetence of offspring. MHC-dissimilar mate preferences may influence the psychology of
  sexual attraction. We investigated whether MHC similarity among romantically involved couples (N =
  48) predicted aspects of their sexual relationship. All women in our sample normally ovulated, and
  alleles at three MHC loci were typed for each person. As the proportion of MHC alleles couples
  shared increased, women's sexual responsivity to their partners decreased, their number of extrapair
  sexual partners increased, and their attraction to men other than their primary partners increased,
  particularly during the fertile phase of their cycles.

Other than that, I can't think of anything else; the rule is pretty much, like attracts like.

A:

However, at least for personality (in this case Big 5, extraversion, neuroticism etc.) there is evidence, that it is actually not similarity that drives relationship satisfaction.
Dyrenforth et al. (2010) who used a rather new methodology called Actor-Partner-Interaction-Models didn't find effects of similarity.
Instead they find actor effects (your personality matters for how satisfied you are in your relationship) and partner effects (your partner's personality matters for how satisfied you are in your relationship).
There are different ways to assess similarity (which the article addresses), but the article sidesteps homogamy and the possibility that people who are in relationships (the population, not the couple) may, by chance (pick any two), be more alike than people who are not in relationships. This is plausible, however, because some personality traits make you less likely to enter and stay in relationships (emotional instability/neuroticism).

Three very large, nationally
  representative samples of married
  couples were used to examine the
  relative importance of 3 types of
  personality effects on relationship
  and life satisfaction: actor effects,
  partner effects, and similarity
  effects. Using data sets from
  Australia (N = 5,278), the United
  Kingdom (N = 6,554), and Germany (N =
  11,418) provided an opportunity to
  test whether effects replicated across
  samples. Actor effects accounted for
  approximately 6% of the variance in
  relationship satisfaction and between
  10% and 15% of the variance in life
  satisfaction. Partner effects (which
  were largest for Agreeableness,
  Conscientiousness, and Emotional
  Stability) accounted for between 1%
  and 3% of the variance in relationship
  satisfaction and between 1% and 2% of
  the variance in life satisfaction.
  Couple similarity consistently
  explained less than .5% of the
  variance in life and relationship
  satisfaction after controlling for
  actor and partner effects.

