Risk mitigation would indicate creating a separate account for each service on each machine. The level of work required to create the accounts necessary is extremely minimal, but the unknown risks that accompany not doing so are quite high, according to Microsoft's own recommendations.
Microsoft Best Practices recommend using separate service accounts for all services.
See http://msdn.microsoft.com/en-us/library/ms144228.aspx#isolated_services for details.
The salient points being:
Isolate Services
Isolating services reduces the risk that one compromised service could be used to compromise others. To isolate services, consider the following guidelines:
Run separate SQL Server services under separate Windows accounts. Whenever possible, use separate, low-rights Windows or Local user accounts for each SQL Server service. For more information, see Configure Windows Service Accounts and Permissions.
There is also a KB talking about securing SQL Server that mentions how to configure service accounts properly:
http://support.microsoft.com/kb/2160720
When choosing service accounts, consider the principle of least privilege. The service account should have exactly the privileges that it needs to do its job and no more privileges. You also need to consider account isolation; the service accounts should not only be different from one another, they should not be used by any other service on the same server. Do not grant additional permissions to the SQL Server service account or the service groups. Permissions will be granted through group membership or granted directly to a service SID, where a service SID is supported. For more details please refer to Books Online Topic Setting Up Windows Service Accounts.
Technet has an article, titled Configure Windows Service Accounts and Permissions at http://technet.microsoft.com/en-us/library/ms143504.aspx that has this to say:
Security Note: Always run SQL Server services by using the lowest possible user rights. Use a MSA or virtual account when possible. When MSA and virtual accounts are not possible, use a specific low-privilege user account or domain account instead of a shared account for SQL Server services. Use separate accounts for different SQL Server services. Do not grant additional permissions to the SQL Server service account or the service groups. Permissions will be granted through group membership or granted directly to a service SID, where a service SID is supported.
"MSA" in the above paragraph refers to "Managed Service Accounts" which is the default for installations on Windows 7 or Windows Server 2008 R2 and above. Managed Service Accounts are defacto unique to each machine.
As an aside, one issue I think about when configuring multiple servers to run under the same service account is account lockouts. If you use a single service account for all SQL Servers, and the service account gets locked out, all your servers might be affected. If you have one account per service, at most one server can be affected by a lockout.
Best Answer
If you check the event log, does the event say something about needing "log on as service" rights?
In my experience you will need to add 'log on as service' rights to the account you select. Although the SQL Server Configuration Manager is supposed to handle this, I've found that it does not always. Try the following: