Deployment stuck at deploying message

Scenario:
While trying to deploy a new solution , I was able to add the solution successfully but then deployment got stuck at deploying message.

Solution:
There is no perfect solution to it but there are couple of things you need to try.

Usually this problem is not with your solution but with any specific server in a multi-server farm. So before you open ticket with Microsoft, make sure you see the same behaviour for your solution on another machine.

Check few things:
1. Go to Central Administration
2. Navigate to Operations > "Global Configuration" > "Timer job status".
3. Look for Jobs name starting with either "Windows SharePoint Services Solution Deployment for "

There will be one entry for each of the front-end servers that the solution is being deployed to or retracted from. Usually one of the entries will say failed and the others will say succeeded so you can use this to help figure out which front-end is causing the problems.

Options:
1. If you are trying to deploy the solution globally, try retracting one by one from each web-application

2. If you are trying to deploying the solution using UI try command line STSADM or vise versa.

3. Try running following STSADM command.
STSADM -o execadmsvcjobs ( On all the servers )

4. If it is getting stuck only on a particular Web Application ( more commonly on Central Web Application ), then try deploying it first on another Web Application.

5. Restart the machine and try one more time.

6. Also if it is multi-server farm, try deploying from other machine.

Article:
STADM Commands