I am very sentimental, and probably in a weird way too.
I too hold onto movies and TV shows that I remember watching with my parents and grandparents. When I originally got into old movies and TV, my parents and grandparents would give me suggestions on what I should watch. I bought shows solely on their enthusiasm to see how I'd like what they used to watch when they were younger. Some of them I have actually parted with because of the language and content, but others -- like GILLIGAN'S ISLAND -- will always be in my collection. My mother and I used to watch a lot of movies together and I've bought them over the years and when I watch them, they bring back fine memories. Movies like SELENA and STEEL MAGNOLIAS bring back good memories of relaxing with my mother and watching TV.
When my wife and I got married last year, I had to get rid of a lot of things I had acquired from other people over the years. These things were mostly knick-knacks or a variety of other things. It was hard getting rid of some of it, but we simply don't have anywhere to store it. Our home is quite small, and we each allotted ourselves a certain amount of space for sentimental belongings.
The one thing I hold onto strongly is pictures. I enjoy taking pictures and having them in photo albums. One day, when people you love have left this world, pictures will be all you have... well, and videos or stuff of that nature. My wife picks at me saying I act like a grandmother having huge photo albums. But I want my pictures and they're not getting thrown away.
For a more weird or unusual example, I take you to yesterday. I met my wife for lunch (we meet half-way on the road between our two jobs) and we ate together. We spent a good 25 minutes together before it was back to work for both of us. We each had a foam cup with drinks in it. She took us with her, and I brought mine back with me. I couldn't throw that foam cup away yesterday afternoon. I was missing my wife bad, and looking at that cup made her feel close to me. Of course, I tossed it in the trashcan at the end of the work day, but I was heading home to her then.
So, yeah, I can be very sentimental and unusually so.