I would say it is better to have a broad base of sporting teams and other sports men and women that you support than just follow Everton, that way you can at least experience some highs.
In footballing terms Real Madrid have always been my second team since the 80's, so the last few years have given me something to cheer about. Not to say it is the same because it's not, but it is better than nothing.
I also support the NY Giants and although recently they are as about as good as Everton, I got to see them lift the super bowl in 08 and 12. Since we last won a trophy in 95 I have also seen Raikkonen, Hamilton (multiple times) and Button win the F1 crowns and obviously a lot more races inbetween. British boxing has been on the up over the last couple of decades, with lots of good champions to follow, esp. Joe Calzaghe. Got to see Wales get to the finals of a competition at last and the rugby team win championships in 05, 08,12 and 13 and some successful British Lions tours. To add to that the tennis with Agassi, Murray and Nadal to name but a few I support and the Ryder cups and the decent results of British athletes in major games I feel that I have had some sporting highs in this lull period in Everton's history.
If I hadn't had that I feel I would be a husk of a man by now. I however would never support another team directly in competition with Everton, but I highly recommend anyone finding a second team that they like and that actually win things.