Database normalization: Describing trait - foreign key to table, or varchar field with value?
You should use a lookup table 


Not all clients will use the ENUM in the application
You will get a reporting or MIS or Excel app connecting at some point
How can do "NOT EXIST" otherwise?
You will be asked this
You won't know about client enum changes
Strings are inefficient compared to a tinyint, especially when you need to index it for your WHERE clause
The data and database will outlive the client application


Also, see these:


"Proper Use of Lookup Tables" 
"INT or CHAR for a Type Field"
"Advantages and Disadvantages to using ENUM vs Integer types?"