I think the accepted answer is in some ways misleading. There are still a good number of psychoanalysts who practice therapy in a way that is fairly orthodox to Freud (or interpretation of his work) and even among those who deviate from the orthodox a lot of work is not grounded in empirical science.
This is acknowledged by its defenders too. Note: That blog post is pure, unfiltered bias and misinformation, please read the comment section and the Coyne piece he's reacting to. It's almost funny how bad the defence is. But even he acknowledges that the scientific method was basically a foreign concept to psychoanalysis practitioners until recently, though he pretends this changed by much. It hasn't, which can be clearly seen from the small number of studies on psychodynamic therapy compared to number of practitioners.
I also think it is important to differentiate between effectiveness, efficience and validity.
Effectiveness - Does it help the psychologically ill?
Yes, there is research to support the notion that psychodynamic therapy helps against some psychological illnesses (more than placebo? - difficult to say). There is considerably more research done on cognitive behavioural therapy (the academically most accepted paradigm). When they are compared, the effect is often equivalent, but this may be due to low statistical power (i.e. sample sizes are usually small, so you find only very large differences and will overlook clinically significant smaller differences). There is less evidence, the stronger the research paradigm (few RCTs with long follow-ups and often the control condition is not evidence-based therapy but a wait list condition, so you have placebo effects all around). For schizophrenia for example, psychodynamic therapy is clearly inferior:
The lack of evidence for the efficacy of psychodynamic therapies in schizophrenia has
also been confirmed by a recent meta-analysis of Malmberg and Fenton. Therefore, the
findings of meta-analyses seem to confirm the theoretical assumptions provided by the
vulnerability-stress-coping models.
Efficiency - Is it good use of therapists' and patients' time?
No, psychoanalytic therapy usually takes much longer and is no more or less effective. A good meta-analysis evaluating long-term psychodynamic therapy (that includes but is not limited to classical psychoanalysis) found it to be worse than shorter, evidence-based therapies. This blog post discussing it also sheds some light on the problems of allegiance bias and using doubtful methods to prove LTPP's worth to insurances in previous meta-analyses. Here's another recent blog post from the same author on an RCT on bulimia where short-term CBT beats LTPP.
Validity - Is it grounded in reality?
A lot of the theory is made up and some of it sounds plainly ridiculous today. To me this is the biggest problem - why build on theories that have been proven wrong in empirical science?
References:
A bit dusty maybe, but we're talking about the old school anyway. Hilgard on Psychoanalysis as Science:
Perhaps the most appropriate retrospective view on Hilgard's lectures on
psychoanalysis comes from Hilgard himself and helps to explain why, in the
face of such poor science, the field
of psychodynamics continues to claim
scientific interest. "A sense of
wonder before the unknown," he wrote,
"appeals to me more than the
confidence that comes from always
having something to say that dissolves
the mystery. To say, 'It couldn't have
been otherwise,' does not itself move
us very far along" (Hilgard, 1974, p.
153).
and for friends of strong language: Is psychoanalysis alive and well at 85? A rejoinder
In therapy you could argue "anything that works and I'll take the placebo effect too, thanks", but why stick with PA when it's clearly not superior & takes more time.
I'm interested in a comparison with homeopathy and whether there is a lobby at work here, too, or if ignorance can just prevail for so long.