Why are not all species hermaphrodites?
Firstly I'll clarify that you are talking about simultaneous hermaphrodites rather than sequential hermaphrodites (1st one sex, then the other e.g. the limpet Patella vulgata).

It is perhaps easiest to address the question by countering it and asking why dioecy (2 sex systems/2 gonochoric types e.g. male and female) is better? As you have pointed out there are obvious advantages to being a hermaphroditic species such as more chance of mating - more likely to provide an advantage at very low population densities where interactions are infrequent.

There are two key disadvantages of hermaphroditism which I will briefly cover but have been discussed in this paper and probably other costs. 

The first is energy costs. Maintaining the capacity to produce male and female gametes will be more costly than maintaining one. This gives the hermaphrodite a fitness disadvantage because energy is rarely an infinite resource. Therefore at higher population densities, when mating opportunities are not rare, the gonochoric individuals will have a higher fitness because they have more energy. Monogamy is also analogous to rare encounters but true monogamy is rare (1 partner for life).

The second disadvantage of hermaphroditism is self fertilisation. This will cause an increase in homozygosity and lead to inbreeding depression (reduced fitness).

So you are right to some extent...


  the hermaphrodite way of reproduction is more successful than the
  "normal" way.


...but the conditions which give rise to an hermaphroditic advantage are restricting. Overall, the above costs, combined with the obvious complexity of evolving the ability to produce male and female gametes, the ability to both fertilise and be fertilised, pregnancy and birth, and mating systems, mean that it is often more beneficial to be a dioecious species. Thus dioecy evolves.



EDIT: Question Raised by @Single_Digit


  I have been pondering this question for a while and I get what RG255
  is saying. I'm just not sure I entirely buy it. Take earthworms, for
  example. They are simultaneous true hermaphrodites (as far as I
  understand). The anatomy doesn't have to be that complex*. They simply
  have two genital openings (one for eggs and one for sperm) and they
  line up in a "69" (excuse the vulgarity) position. This should, in
  theory, minimize the inbreeding depression. However, it doesn't
  eliminate the maintenance of two sets of reproductive systems. But
  most organisms are not internally fertilized mammals with wildly
  complicated systems of internalized embryonic care. Most species lay a
  pile of eggs that a male squirts sperm on or squirt eggs while the
  male squirt sperm and then they hope for the best.
  
  I would think the advantages of simultaneous parenting (after all,
  many MANY species' males don't provide much in the way of child care)
  and its fitness advantage would vastly outweigh the burden of a second
  set of reproductive organs.
  
  With that said, I don't have a better explanation, but I find the
  question a very interesting one. The linked article is pay-walled,
  aside from the abstract, but I still disagree with some of its tenets.
  To me true hermaphroditism should be very common (I realize it isn't)
  in species that don't need two parents to raise offspring, but do
  benefit from some (as in one parent's) parental care. I recognize that
  it would do little to help species that merely dump gametes and leave
  because specialization of one reproductive system would likely do the
  job better and both genders equally contribute under that type of
  system.
  
  So, RG255 convince me! Clearly there are good reasons, since gender
  (or asexual repr) is the norm, but I need more/better evidence.
  
  
  
  Yes I realize they would need separate internal anatomies for each type of gamete, but still...
  
  


My response:


  You have presented one example of hermaphroditism and used that as
  evidence that all species should be hermaphrodites. Earthworms are
  small slow creatures living in soil, I don't imagine they have high
  rates of encounter, and therefore low rates of encountering the
  opposite sex, therefore hermaphroditism would be favoured as discussed
  above. 
  
  Further, you say most species are external fertilisers (do you
  have a reference for this?) and therefore it is not costly be a
  hermaphrodite. I don't see your logic there, the cost is not
  necessarily to do with the cost of bearing child, producing &amp;
  maintaining the gonads and gametes is also a costly process. I would
  argue that this is extremely complex. This is not just on a
  morphological level but also physiological: in non-hermaphroditic
  species the sexes have very different, and often, conflicting gene
  expression and hormone production patterns. Hermaphrodites would not
  be able to optimize to the fulfilling both the male and female roles.
  
  Finally, you pointed out that the worms do not inbreed. Inbreeding
  avoidance does not have to be the cause of the hermaphroditism
  persisting, if the environment/other factors favour hermaphroditism. I
  never said that both were simultaneously necessary. 
  
  I hope this
  clarifies it for you, if not please expand as to why, I am on here
  because I want to help people understand biology properly!


Further response from @single_digit:


  Well fair enough about my external fertilizers comment. I don't have a
  reference, but I was thinking all multicellular life and I'd have to
  imagine that when you factor in plants, that external fertilization is
  relatively the norm (as is hermaphrodism (dioecy) for the plants). As
  to earthworms, I disagree about your description of them. Their
  densities are actually pretty high, so I'd wager they encounter each
  other frequently, so I'm not sure where that leaves them in terms of
  pressures for hermaphroditism. Your point on the physiologic/hormonal
  issues of maintaining the systems is one I haven't previously
  considered. I honestly don't have any clue as to how daunting (or
  simple) that is, but I'd imagine that the sophistication of the
  systems would play a pretty key role. Makes me wonder how much this
  has been researched in true hermaprhodites. I suppose the main thing I
  keep coming back to is the overwhelming disadvantage gender has in
  terms of potential to create offspring. Males in many (most?) species
  essentially act as little more than sperm donors, thus half the
  individuals have effectively zero fitness. That just seems like an
  overwhelming advantage for hermaphrodites.


My Response


  Why do you consider half of the individuals to have zero fitness?
  Fitness is widely accepted as the number of offspring a parent
  produces because this is directly related to number of copies of their
  genes passed to the next generation. Sperm donor type males achieve
  increased fitness by mating as do females - with out the male they
  would never be fertilized. The key disadvantage of dioecy is the
  halved (assuming equal sex ratio) frequency of potential encounters
  that could lead to mating. The general disadvantages of
  hermaphroditism are inbreeding depression and high cost &amp; complexity.


Single_digit:


  Zero fitness isn't exactly correct, but if we look at parental care as
  conveying a survival advantage for K selected species, and huge
  numbers of offspring conveying an advantage for r-selected species
  (obviously the type of env affects this) does a deadbeat dad really
  optimize for either of these? Passing on genes is fine, but if
  offspring survival is low, does it matter? Does it simply boil down to
  the maintenance of two repr systems plus decreased fitness from
  inbreeding vs the increased reproductive success from extra child
  care? Or is there more?


My response:


  r/K selection theory has generally been disregarded in the
  evolutionary biology community due to the substantial evidence against
  it so it is unhelpful to think of selection in this way. As long as
  the 2 sexes strategy is more successful at passing on genes than a
  hermaphroditic strategy it will (should) prevail. Dioecy will be more
  successful if the hermaphroditism introduces to much cost through
  production and maintenance of sexual organs/gamete and inbreeding
  whilst not attaining substantial gains from higher potential mating
  frequency.


@Single_Digit


  Interesting about r/K selection. I hadn't heard that. Do you have any
  links? I'd be curious to learn more there. I incorrectly earlier made
  a comment about dioecy where I meant monecy. But this seems to beg the
  question, why is monecy/hermaphroditism so much more prevalent in
  plants? Obviously there are different survival pressures, but I'd
  think the same basic principles would apply as in animals, but the
  condition seems to be far more common than in animals.


My Response


  I seem to remeber there being a reason in plants, don't
  have time to look it up right now. The work about r/K selection was
  Reznick/Stearns/Charlesworth. Reznicks is the most recent and more
  overview type paper - best place to start:
  http://www2.hawaii.edu/~taylor/z652/Reznicketal.pdf