I would say bookkeeping is the number one thing. A lot of translators spend hours and hours on receipts and invoicing and for those that have a lot of work, that's just lost revenue. At one point I was spending 30 hours a month on bookkeeping because it is not my strength. I also made the mistake of assuming that I would have to pay a bookkeeper quite a lot of money because I was basing it on the time I was spending, not the time a professional would spend. Now I have a better system, or rather my bookkeeper does, and I pay for around 2 hours a month. Not to mention the stress relief for me was priceless.
What can be outsourced also depends on how booked a translator is. If you're extremely busy, it's important not to fall into the trap often created by working from home. I wrote an entire blog post recently about how interruptions affect productivity and in researching for it, I found the effects were actually a lot more significant than I thought. I may have felt ridiculous outsourcing my laundry since I work from home, but I saw a boost in productivity because it was one less thing I had to stop and do which paid for the additional expense immediately.
Childcare is another. A lot of translators who are parents do not have childcare while they work. One of my clients ended up hiring a full time nanny after she ran the numbers and realized how much money she was losing because she was trying to multitask with her kid...not to mention the stress of trying to entertain and care for him while trying to focus on a translation.
Shopping is another example, although this is more along the lines of automation than outsourcing. I use Amazon Prime to order everything from computer equipment to hand soap and toothpaste. I save tons of time (and frustration) that would have otherwise been spent on trips to stores, searching for products, and standing in line.