Cystic fibrosis is the only pulmonary condition FDA-approved for inhaled tobramycin, but there are tobramycin has also been used for non-cystic fibrosis bronchiectasis. While data is limited, tobramycin has potential use as a long-term nebulized antibiotic if patients are chronically colonized by P. aeruginosa and in patients who experience 3 or more exacerbations a year that cause significant morbidity. Inhaled tobramycin has also been studied as post-transplant prophylaxis in patients with pretransplant infection with multidrug-resistant organisms (P. aeruginosa or Burkholderia cepacia). A small uncontrolled study has also evaluated tobramycin inhalation for overlapping bronchiectasis with purulent sputum production and chronic infection with Pseudomonas aeruginosa. [1-3]
A meta-analysis reviewed five randomized controlled trials on the use of inhaled tobramycin in patients with non-cystic fibrosis bronchiectasis. The analysis demonstrated a high heterogeneity among the studies (I^2=75%), so the authors did not report the overall pooled results. Two studies demonstrated decreased P. aeruginosa sputum density compared to placebo. The results of three studies reported inhaled tobramycin to be associated with P. aeruginosa eradication after a median of 4.3 weeks (odds ratio 4.87; 95% confidence interval 1.04 to 22.77; I^2=40%). The data also reports antibiotic resistance to tobramycin, suggesting inhaled tobramycin leads to resistant P. aeruginosa strains. Additionally, tobramycin showed an increase in all non-fatal adverse effects including bronchospasm that lead to subject withdrawals from the interventional group. The authors conclude there is not enough evidence to confirm the benefit of inhaled tobramycin. 
A 2011 poster abstract presents a pilot study of inhaled tobramycin to prevent airway stenosis after lung transplantation. Of 22 patients who received inhaled tobramycin, (2×80mg for the first 7 postoperative days), 7 patients (31.8%) developed airway complications. Of a historical cohort matched for age, gender, and diagnosis lead to transplant, 15/22 patients (68.2%) who did not receive post-transplant tobramycin developed airway complications. This resulted in a significant decrease in the development of postoperative stenosis with inhaled tobramycin (P=0.034). 
A case report described a 63-year-old man who developed renal toxicity after inhaled tobramycin following bilateral lung transplantation because of idiopathic pulmonary fibrosis. The patient had multiple bronchial infections caused by Pseudomonas aeruginosa, so inhaled tobramycin was started at a dose of 300 mg BID. Ten days after starting tobramycin, his creatinine level rose from 2.5 to 3.5 mg/dL despite cyclosporine adjustments. Tobramycin was withdrawn, and his creatinine decreased to his previous value within 1 week. 
A second case described a 55-year-old man who received a lung transplant due to emphysema. Inhaled tobramycin was started because of repeated bronchial infections by P. aeruginosa following a bronchiolitis obliterans diagnosis. After starting tobramycin, his creatinine rose to 4 mg/dL, potassium levels reached 7 mEq/L, and the patient required temporary hemodialysis. His renal function returned to normal 15 days after tobramycin was stopped.