Iam involved in running multiple regression, where explanatory variables include (year), should I use this variable as it is (2005.2006....) or should it be coded as(1,2,3...) ?
You need to declare it using dummy variables. Coding as 1,2,3 does not guarantee that it will enter as a categorical variable into regression model. Make sure that your software understands that it is a categorical variable, not a continuous one. You may need to manually introduce dummy variables for this variable depending on the software and procedure you are using.
Iam using SPSS to run the multiple regression model, where the variable called year is staring from 2005:2015, How can I make it a dummy variable? and How can I make sure that SPSS understand that it is a categorical variable not continuous?
Making it dummy is tedious. You need to introduce 15 dummy variables. Instead use General Linear Model -> Univariate menu and put year into fixed factor box and run regression through this window. That does the job.