I can't say whether Viktor Frankl is respected by modern psychologists on average, or how respected he is. Anecdotally, I have heard of both Frankl and logotherapy, but not enough to know much more than that they exist. The real question, though, is whether there is any empirical support for logotherapy, and overall, the evidence (for or against logotherapy) I could find is very limited.
Empirical support for logotherapy
At the very least, there has been a limited amount of recent research. Psychometrically, a 2004 review of logotherapeutic measures reported that the Purpose-in-Life test (PIL), the Life Purpose Questionnaire (LPQ), the Seeking of Noetic Goals test (SONG), and the Meaning in Suffering Test (MIST) were internally consistent (Schulenberg, 2004).
Logotherapy also appears to have some empirical support as a treatment for a few specific issues, such as reducing self-reported suffering in adolescents with terminal cancer (Kang et al., 2009), reducing self-reported sense of meaninglessness in people with paralysis (Julom and de Guzmán, 2013), and assisting with the treatment of PTSD (Southwick, Gilmartin, Mcdonough and Morrissey, 2006).
- Julom, A. M., & de Guzmán, R. (2013). The effectiveness of logotherapy program in alleviating the sense of meaninglessness of paralyzed in-patients. International Journal of Psychology and Psychological Therapy, 13(3), 357-371.
- Kang, K. A., Im, J. I., Kim, H. S., Kim, S. J., Song, M. K., & Sim, S. (2009). The effect of logotherapy on the suffering, finding meaning, and spiritual well-being of adolescents with terminal cancer. Journal of Korean Academy of Child Health Nursing, 15(2), 136-144.
- Schulenberg, S. E. (2004). A Psychometric Investigation of Logotherapy Measures and the Outcome Questionnaire (OQ-45.2). North American Journal of Psychology.
- Southwick, S. M., Gilmartin, R., Mcdonough, P., & Morrissey, P. (2006). Logotherapy as an adjunctive treatment for chronic combat-related PTSD: A meaning-based intervention. American Journal of Psychotherapy, 60(2), 161.