Ah, to be famous on Tumblr. You'd get thousands of followers, hundreds of adoring asks and fan mails, countless likes and reblogs to your every post. With millions of blogs and billions of posts on Tumblr, no foolproof strategy exists that guarantees people will follow your blog. You can, however, improve your odds.
Find Your Audience
You may love lots of interesting things, but making a blog encompassing all of them is unlikely to get you many followers. Think about it -- even your best friends don't love all the same things you do. The more subjects you post about, the more likely it is that people won't follow you because they'd end up having to scroll past a lot of what they would perceive as uninteresting posts just to get to the ones they care about. Keep your blog's focus narrow, but not so narrow you have little content and no audience -- think "tigers being cute" rather than "baby white tigers playing with red balls." You can always make one or more side blogs for everything else.
Tag, You're It
Rambling on in the tags can be great fun, but if nobody can find your blog, nobody will follow it. Use tags first and foremost to identify the subject of each of your posts, so people who track related tags or search for them will find your posts. You likely already have a good idea of the main tags for your blog's subject. If you don't, investigate -- look at well-liked blogs on the subject and see what tags they use.
Like almost everywhere else, few people will notice you if you just hang around the edges and stay quiet. Jump into the community -- follow other blogs, like posts, reblog and add your two cents, send pertinent asks and the list goes on. Do keep in mind, though, that other people aren't obliged to follow your blog just because you follow theirs. Smaller blogs with few followers will likely follow you back, but the larger ones very well may not, if only because following several thousand people would make keeping track of that dashboard a nightmare.
Think about the blogs you follow and consider the reasons why. All of them are more or less guaranteed to reblog at least some content from other blogs, but they all likely contain a fair amount of original content you can't find anywhere else. If you regularly post interesting, unique content, people will be more likely to follow you than if you simply reblog other blogs' content.
Rarely updated blogs are boring to follow. If your posting schedule slows or stops completely, you are likely to lose followers; if it's slow to begin with, you are unlikely to gain any. If you know you're going to be too busy to post or away from the computer for more than a few days, set up automatic posting using Tumblr's queue feature. You can automatically publish up to 50 posts a day at the times you specify, keeping your readers entertained while you're out living your life. If you prefer, you can also schedule specific posts to publish on an exact date and time rather than filling your queue.