If you're referring to something already mentioned:
* That - "I saw a dog. That dog was brown."
* This - "I have a book. This book is very old."
* These / Those - "I saw some apples. Those apples were red."
If you're referring to something specific but not previously mentioned:
* A particular - "A particular type of flower grows here."
* A certain - "A certain kind of bird sings in the morning."
* The very - "This is the very book I was looking for."
If you're referring to something in general:
* Any - "Any cat can learn to sit."
* Every - "Every person has their own unique story."
* All - "All dogs are mammals."
Other possibilities:
* Specific - "There is a specific reason I chose this path."
* Particular - "I have a particular fondness for old movies."
Ultimately, the best alternative to "the" depends on the specific context of your sentence.